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Question 1180841: Jim, Jane, Jen, Josh, Josiah and Judy are members of the same club. Determine the number of ways of selecting :
(a) a 3-member committee , is it 10 C 3?
(b) a 3-member committee with at least one girl
(c) two people to be chair and vice, is it 10 C 1 x 9 C 1?
(d) a 4-member committww with 2 girls and 2 boys, is it 3 C 2 X 3 C 2 ??
Click here to see answer by ikleyn(52776)

Question 1180849: A set of flash cards consists of 15 red, 12 blue, 10 black and 12 yellow cards. The cards in each colour are numbered from 1 through 15.
(a) How many groups of 6 cards can be selected from the entire set?
(b) How many groups of 6 can be selected from the red cards?
(c) How many groups of 24 cards can be selected from the entire set if there must be six of each colour?
Thank you in advance for any help:)
Click here to see answer by ikleyn(52776)

Question 1180815: Consider the distinct arrangements of the 12 letters in the word PALEOZOOLOGY
How many distinct arrangements have none of the 5 letters G, L, L, P, Z adjacent?
I have no idea where to start. Any help is appreciated.
Click here to see answer by Edwin McCravy(20054)

Question 1181276: A group of Mathematics faculty at the local college consists of 10 women and 8 men. Four people are to be selected to go to a conference.
How many different ways can a group of four people be selected from this group of 18?
In how many ways can four women be chosen from the group of 10 women ?
What is the probability that all women will be chosen to attend the conference? (enter reduce fraction or decimal)
Click here to see answer by ikleyn(52776)

Question 1181318: How many four-digit numbers can be
formed using the digits 1, 2, 3, 4, 5, 6, if the four-digit number is odd?
(Repetition is allowed)
Click here to see answer by mccravyedwin(406)

Question 1181314: Zoe wants to give 3 of her 12 favorite toys to her friend. In how many ways can she choose 3 toys to give her friend?
Click here to see answer by Edwin McCravy(20054)

Question 1177266: From 5 consonants and 4 vowels, how many words can be formed (with or without meaning) using 3 consonants and 2 vowels such that vowels are always together?
Click here to see answer by Edwin McCravy(20054)

Question 1181368: if a class has 28 students in how many different arrangements can 5 students gives a presentation to the class
Click here to see answer by ikleyn(52776)

Question 1181398: In a dance contest, each participating group must perform 3 kinds of dance. If there are 4 choices for ballroom dance, 8 choices for foreign dance, and 5 choices for hip-hop, in how many ways can a dance group selected their piece?

Show the solution pleasee!!!
Click here to see answer by ikleyn(52776)

Question 1181430: How many different 4-digit even numbers can be formed from the digits 1,3,5,6,8, and 9 if no repetition of digits is allowed?
Click here to see answer by ikleyn(52776)

Question 1181512: How many "words" can be made from letters of the word CATERING using different permutations, according to the following rules.
1. Two vowels and two consonants must be used without repetition.
2. Three vowels and one consonant must be used, without repetition.
3. At least two vowels and at least two consonants must be used, without repetition, in six-letter words.
The answer for 1 is too 720. Answer for 2 is 120 and answer for 3 is 18 000. I know the answers but I don't know how to work it out.

Click here to see answer by ikleyn(52776)

Question 1181914: A total of 56 different two item permutations can be created from a pile of clothes containing?
A. 9 garments
B. 8 garments
C. 10 garments
D. 20 garments
Click here to see answer by Edwin McCravy(20054)

Question 1181974: Ron is having a dinner party. He invites 7 out of his 10 friends. In how many ways can he choose his guests if two of them, Al and Sue, must attend together or not at all?
Click here to see answer by ikleyn(52776)

Question 1182131: I saw this solution online from a tutor (ikelyn). I think there's a mistake in it and i need to make sure I'm right. So in case b in this solution. Shouldn't the equation be 8*8*7*4 = 1792? (4 because there are 4 different possible digits?) In the solution it says 8*8*7 = 448.
The solution:
How many 4-digit even numbers can be formed from the digits 0 to 9
if each digit is to be used only once in each number ?
Solution
The fact that the number is an EVEN number means that the last digit is one of 5 even digits 0, 2, 4, 6, or 8.

In my solution, I will consider two cases separately:
case (a): the last digit is 0 (zero),
and
case (b): the last digit is any of the remaining 4 even digits 2, 4, 6 or 8.

Case (a): the last digit is 0 (zero)
Then the first (most-left) digit is any of 9 remaining digits;
the second digit is any of remaining 8 digits;
the third digit is any of remaining 7 digits.

So, the total number of possible options is 9*8*7 = 504 in this case.

Case (b): the last digit is any of remaining 4 digits 2, 4, 6 or 8.
Then the first (most-left) digit is any of 8 remaining digits (keep in mind that the leading digit CAN NOT be 0 (!));
the second digit is any of 8 remaining digits (zero is ALLOWED in this position);
the third digit is any of 7 remaining digits (zero is ALLOWED in this position).

So, the total number of possible options is 8*8*7 = 448 in this case.

Thus the total number of possibilities is 504 + 448 = 952.

ANSWER. 952 four-digit even numbers can be formed from the digits 0 to 9 if each digit is to be used only once in each number.
Click here to see answer by math_tutor2020(3816)

Question 1182133: Hello, I just need someone to confirm my answers for these questions (if I'm wrong someone please help and correct me thank you:
In one section of a math test paper, a student answers 3 out of 4 questions in that section. In How many ways can this section be answered if different orders in which the questions are answered count as different ways.
My answer is 4*3*2 = 24

In how many ways can 4 boys and 2 girls seat themselves in a row if
(a) the 2 girls are to seat next to each other
(b) the 2 girls are not to seat to each other
(c) the 2 girls are to be separated by 2 boys between them
for (a) I did 4!*2!*6 ( 4! is for the boys, 2! for the girls and 6 positions the girls can start at). This for me is a bit tricky for some reason.
for (b) I did 6! - 2!(6-2+1)! = 480
for (c) I did 4! * 2! * 3 (4! from the boys. 2! from the girls and 3 from the fact that there are only 3 cases of this that can be happened)
in how many ways can 5-digit numbers be formed using the digits 0,1,3,4,5 if
(e) no repetition of digits is allowed
(d) repetition of digits is allowed

for (e) I did 4*4*3*2*1 = 96 (4 at first because zero is not allowed in the first digit of a number)
for (d) i did 5*5*5*5*5

Click here to see answer by greenestamps(13198)

Question 1182155: Hello, I found this question in the permutations and combinations chapter of my math's textbook. I need help to understand and solve it.
Find the probability of obtaining exactly:
(a) 3 heads from 5 tosses of a coin
textbook answer says its 5/16, but shouldn't the answer be 3/10? (3 the event and 10 all possibilities including heads and tails)
There are more questions like these like:
(b) 2 heads from 8 tosses of a coin
(c) 6 heads from 8 tosses of a coin
(d) 2 heads from 4 tosses of a coin
(e) 10 heads from 20 tosses of a coin

answers for these are:
(b)7/64
(c)7/64
(d)3/8
(e) 184756/1048576

Click here to see answer by math_tutor2020(3816)

Question 1182241: Hello, I just need someone to check my answers for these questions. Thank You.
1. In how many different ways can seven books be arranged on a shelf of two particular books must always be next to each other?
for this I did 5! * 2! * 6 (5! from the 5 left over books and 2! from the two books, 6 positions for the girls to start with)
2. How many ways can five pieces of candy be divided between two children if each child receives at least one piece of candy?
There are two cases for this question.
1st case:
One child gets one candy, and they other one gets the rest. So
I did 5 choose 1 times 5 choose 4 which is 25 ways.
2nd case:
one child get 2 candies, while the other one get 3.
So I did 5 choose 2 times 5 choose 3, which is 100 ways.
Finally I add these values up 100 + 25 = 125
2. A team of five is to be chosen from a group of eight students. The two tallest students cannot both be on the team. How many different teams can be formed?
for this one, I did 8 choose 5 minus 6 choose 3 (because the two tallest are removed), which equals t0 56 - 20 = 36.
3. A group of 8 people consists of 6 adults and two children. Calculate the number of ways in which five people can be selected from these 8 in each of the cases:
(a)order of selection is unimportant
(b)the five people are selected in a definite order (I don't understand this one)
(c)order of selection is unimportant and at most one child may be selected.
for (a) I did 8 choose 5. 56 ways.
(b) I don't understand b at all
(c) I did 7 choose 4 because, one child is guaranteed to be selected. 35 ways.

Click here to see answer by ikleyn(52776)

Question 1182280: A committee of 5 people is going to be chosen from a group of 8 women and 10
men. How many different committees are possible if the committee must
contain at least 1 woman and at least 1 man?
How many committees are possible if the committee must have 3 women and 2 men?
How many committees are possible if the committee must have more women than men?
Click here to see answer by Edwin McCravy(20054)

Question 1182202: Determine the number of three figures numbers between 100 and 999 inclusive, have only two consecutive figures identical. (I don't really understand this question.)
Click here to see answer by greenestamps(13198)

Question 1182621: -k-(-8k)
Click here to see answer by MathLover1(20849)

Question 1182644: Consider the 720 permutations of the numbers 1, 2, 3, 4, 5, 6. In how many of
these permutations does 1 appear next to 2 or 3 appear next to 4 or 5 appear
next to 6?
Click here to see answer by greenestamps(13198)

Question 1183008: Megan is planning a long-awaited driving tour, which will take her and her family through three different states. Megan is interested in seeing 14 monuments, three of which are in the first state, Six of which are in the second state, and five of which are in the third state. However, she only has time to see three of them. In how many ways can the three monuments chosen include sites in fewer than all three states?
Click here to see answer by greenestamps(13198)

Question 1183043: In how many ways
Click here to see answer by ikleyn(52776)

Question 1183044: How many ways can we select three books each from a different subject from a set of six distinct history books, nine distinct classics books, seven distinct law books, and four distinct education books?
Click here to see answer by ikleyn(52776)

Question 1183045: a club consisting of six distinct men and seven distinct women;
a.) how many ways can we select a committee of five persons?;
b.) In how many ways can we select a committee of three men and four women?
Click here to see answer by ikleyn(52776)

Question 1183042: Suppose that a pizza parlor features four specialty pizzas and pizzas with three or fewer unique toppings (no choosing twice!) chosen from 17 available toppings. How many different pizzas are there? (3pts)
Click here to see answer by ikleyn(52776)

Question 1183064: how many strings can be formed by ordering the letters ABCDE if: (1pt each)
a.) A appears before D;
b.) Contains either the substring DB or the substring BE or both

Click here to see answer by ikleyn(52776)

Question 1183066: In how many ways can we select a Representatives of 4 SPEAKS, 3SAMASA, and 2 Independents from a group of1 0 distinct SAMASA, 12 distinct SPEAKS, and 4 distinct Independents?
Click here to see answer by ikleyn(52776)

Question 1183179: Twelve girls try out for the hockey team. Two play goal, four play defence, and the rest play forward. How many different starting lineups could the coach choose if she needs 1 goalie, 2 defence, and 3 forwards?
Click here to see answer by greenestamps(13198)

Question 1183178: A sportswriter makes his pre-season picks for the top ten teams finish. If there are forty teams, how many different lists could there be?
Click here to see answer by greenestamps(13198)

Question 1183400: Suppose you have n different pairs of socks (n left socks and n right socks, for 2n individual socks total) in your dresser. You take the socks out of the dresser one by one without looking and lay them out in a row on the floor. What is the probability that no two matching socks are next to each other?
Click here to see answer by robertb(5830)

Question 1178038: There are 11 girls and 9 boys in Form 1A and 10 girls and 9 boys in Form 1B in a school. Eight students are to be selected from each Form to take part in an essay competition. Find, correct to three decimal places, the probability that equal number of girls and boys will be selected from:
(a) form 1A
(b) each form
Click here to see answer by robertb(5830)

Question 1183692: A lot consists of 20 defective and 80 non-defective items from which two items
are chosen without replacement. Events A & B are defined as A = the first item
chosen is defective, B = the second item chosen is defective
a. What is the probability that both items are defective?
b. What is the probability that the second item is defective?

Click here to see answer by ikleyn(52776)

Question 1183691: Women’s shoes are manufactured in sizes 2, 3, 4, …, 8. Size 5 is suitable for a foot of length ranging from 9.25 inches to 9.5 inches. If length of women’s foot are normally distributed with mean 9.4 inches and standard deviation 0.25 inches, how many pairs of size 5 are required out of every 10,000 pairs manufactured?
Click here to see answer by Boreal(15235)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035