Questions on Algebra: Combinatorics and Permutations answered by real tutors!

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Question 1193547: A man possesses 24 books, all different. In how many ways can he arrange 12 of them on a shelf?
Click here to see answer by greenestamps(13198)

Question 1193597: The United States Senate Committee on Commerce, Science, and Transportation consists
of 23 members, 12 Republicans and 11 Democrats. The Surface Transportation and
Merchant Marine Subcommittee consists of 8 Republicans and 7 Democrats. How many
ways can members of the Subcommittee be chosen from the Committee?
Click here to see answer by ikleyn(52776)

Question 1193599: How many different “words” can be formed by using all the letters of each of the
following words exactly once?
a. “ALICE”
b. “APPLE”
Click here to see answer by ikleyn(52776)

Question 1193777: Distinguishable Ways to Arrange the Word ILLINOIS
Click here to see answer by Edwin McCravy(20054)

Question 1193777: Distinguishable Ways to Arrange the Word ILLINOIS
Click here to see answer by ikleyn(52776)

Question 1193664: A normally distributed data set of 500 values has a mean of 35 and a standard deviation of 7. Which is closest to the probability that a value in the data set will fall between 42 and 46?

Click here to see answer by Boreal(15235)

Question 1193822: A fair decimal die is rolled three times. What is the probability that
All three outcomes represent odd numbers?
Answer: 1/8
The digit 1 occurs at least once?
Answer: 22/125
Click here to see answer by math_tutor2020(3816)

Question 1193829: 12 balls — 4 red, 4 white, and 4 blue.
If three balls are drawn at random out of this box one at a time without replacement, what is the probability of obtaining
3 white balls?
Answer: 1/55
4/12 * 3/12 * 2/10
3 balls of the same color?
Answer: 3/55
p{(w,w,w),(R,R,R),(B,B,B)}
1/55 + 1/55 + 1/55
Are my answers correct? Thanks

Click here to see answer by Edwin McCravy(20054)

Question 1193828: There are two red, three black, and five white balls. If any two balls of the same color are indistinguishable, how many distinct patterns can be made by lining them up from left to right?
Click here to see answer by Edwin McCravy(20054)

Question 1193823: A decimal die is tossed four times, thus producing a block of four random digits.
The block is said to be an increasing block if it is of the type 1479, that is, if from the second digit on, each digit stands for a larger number than the previous digit does.
What is the probability of obtaining an increasing block?
Click here to see answer by ikleyn(52776)

Question 1193840: With a view to estimating how many fish there are in a big lake, 25,000 fish are tagged and then released.
After some time 20,000 fish are captured and it is found that 50 of them are tagged.
Give an estimate of the number of fish in the lake.
50/20000= 1/400
25000 * 1/400= 10 000 000

Click here to see answer by josgarithmetic(39616)

Question 1193842: Carl claims to have so delicate a palate that he can tell by tasting from which brand of juice L and R a given sample originated.
Carl is presented with eight cups filled by spinning a spinner with choices L and R .
p(L)= 1/4
p(R)= 3/4
Carl simply predicts the outcome which has the higher probability. What is the probability that his guess will be correct?
Click here to see answer by ikleyn(52776)

Question 1193861: How many five-digit numbers may be made from the five digits 1, 2, 3, 4, 5.
If a digit may be used exactly once and neither of the first two digits can be 5?
Click here to see answer by ikleyn(52776)

Question 1193865: Determine the number of combinations of 20 things, taken four(4) at a time
Click here to see answer by ikleyn(52776)

Question 1193865: Determine the number of combinations of 20 things, taken four(4) at a time
Click here to see answer by Edwin McCravy(20054)

Question 1193864: Determine the number of permutations 20 things, taken four(4) at a time
Click here to see answer by ikleyn(52776)

Question 1193862: Three hunters each have a probability of 4/5 of hitting a target.
If each hunter fires exactly one shot at the target, what is the probability that it will be hit at least once?
I'm not sure if this is correct.
Two choices (hit or miss)
3 hunters
total outcomes 2^3 = 8
At least the target hit once,
so could be
- hit 1 time (3 take 1)= 3
- hit 2 times (3 take 2) =3
- hit 3 times (3 take 3) =1

p{(hit 1 time), (hit 2 times),(hit 3 times)}
3/8 + 3/8 + 1/8 = 7/8
then,
7/8 * 4/5 =28/40
= 7/10

Please help, thanks.

Click here to see answer by ikleyn(52776)

Question 1193874: A coach must reduce his basketball team from 13 players to 11 players.
Among how many different final teams has he to choose?
13C11= 13C2
= 13 x 12/2!
= 156/2
= 78
What is the probability that a particular player, S, will be chosen to remain on the team?

Click here to see answer by math_tutor2020(3816)

Question 1193875: On each day of a certain week, one of five people is selected at random.
What is the probability that on the first three days of the week
a- different people are chosen?
b- the same person is chosen each day?

Click here to see answer by ikleyn(52776)

Question 1193916: How many different four-digit numbers are possible if each digit of the number is either 0,1,2,3,4 or 5, and numbers starting with 3 cannot be even?
The textbook answer is 972.
Can someone tell me how to solve this problem?
Click here to see answer by Edwin McCravy(20054)

Question 1193917: Lucinda goes to the local pizzeria for dinner with a group of friends. The menu offers 4 types of soup, 5 main meals, 6 desserts and 3 different types of drinks. Lucinda will order 2 different courses and a drink. How many dinner options does she have?
Textbook answer is 222.
Can someone explain the solution of this problem?
I thought of
4*5*6 = 120 (for the first course)
3*4*5 = 60 (for the second course)
then i add them up to 180 and multiply it by 3 to get 540.
Click here to see answer by greenestamps(13198)

Question 1193915: From a collection of 10 different fonts, 3 different ones must be chosen to be used on a webpage: one for heading, one for standard text and one for quotations. Determine the number of different ways the fonts can be chosen and allocated, given that one of the ten fonts, MT Heading, is only appropriate for the heading.
The answer is 576.
Can someone please explain how to get this answer. Thank you.
Click here to see answer by greenestamps(13198)

Question 1193951: A binary string is an ordered sequences of 0's and 1's (for example, 0100101). Determine the number of binary strings there are consisting of five 0's and three 1's.
Textbook answer is 56.
Can someone help me solve this problem? Thanks.

Click here to see answer by Theo(13342)

Question 1193952: an optical shop sells 10 types of plastic frames, 12 types of rimless frames and 9 types of metal frames. each pair of glasses can be matched with normal lens, non reflective lens, or anti scratching, non reflective lens. Molly is going to buy a pair of glasses from the shop how many choices does she have?
Click here to see answer by Theo(13342)

Question 1193982: A photograph of a diving team is to be taken with the team members in two rows. The team has four girls and two boys. The back row has four places while the front row has the coach in the middle with one diver to the left and one diver to the right. How many ways can the divers be arranged in the photograph if the boys and girls are to alternate in the back row?
The textbook answer is 96.
Can someone explain the solution of this problem? Thanks.
Click here to see answer by math_tutor2020(3816)

Question 1194074: Four girls and three boys are seated randomly in a row. Calculate the following probabilities.
(a) The girls occupy the first three places.
(b) They are arranged to alternate girl, boy, girl, etc.
Answers
(a) 4/35
(b) 1/35
Can someone explain the answers? Thank you.

Click here to see answer by ikleyn(52776)

Question 1194073: if the letters A, B, C, D, E and F are randomly arranged, calculate the probability that the letters A and B will be next to each other?
Textbook answer is 1/3.
Can someone help me solve this problem? Thanks.

Click here to see answer by ikleyn(52776)

Question 1194072: Seven individuals chosen at random from a group of ten individuals are seated at random along one side of a long table. Calculate the probability that a particular individual is chosen to sit at the table, and is placed in the middle seat.
Textbook Answer is 1/10
Can someone explain the solution? Thank you.
Click here to see answer by greenestamps(13198)

Question 1194109: A standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each suit containing 13 cards (ace, two through ten, jack, queen, and king) for a total of 52 cards in all.
How many 7-card hands will consist of exactly 3 kings and 3 queens?
Click here to see answer by math_tutor2020(3816)

Question 1194203: In a class of 18 students made up of 10 females and 8 males, a slate of officers (class president, class secretary, and class treasurer) will be selected. Assuming that a student may not hold more than one office, how many of these slates will be all male?
Click here to see answer by math_helper(2461)

Question 1194204: In how many ways can a committee of three men and four women be formed from a group of 10 men and 10 women?
Click here to see answer by ikleyn(52776)

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