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

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Question 382618: in how many ways can a committee of 4 men and 5 woman be formed from a group of seven men and seven woman?
Click here to see answer by robertb(5830)

Question 382715: how many 3 digit numbers can be formed is the leading digit cannot be 0?
Click here to see answer by richard1234(7193)

Question 382947: How many different four-letter words can be formed from the letters: a,b,c,d,e,f, and g if no repetition of letters is allowed ?
Click here to see answer by edjones(8007)

Question 382852: A group of 14 must select a president, a vice-president, a treasurer and a secretary. How many ways can this be done?
Click here to see answer by nyc_function(2741)

Question 383270: (2n+1)!/(n+2)! * (n-1)!/(2n-1)!=3/5 what is n?
Click here to see answer by stanbon(75887)

Question 383380: what is 15 girls out of 40 students
Click here to see answer by solver91311(24713)

Question 383445: In how many ways can 5 people be assigned to seats in a 9 seated room?
Click here to see answer by robertb(5830)

Question 383823: What is the sum of the numbers in row 5 of Pascal's triangle?
Click here to see answer by edjones(8007)

Question 383822: In a survey with 54 member, 20 were taking mathematics, 35 were taking English, and 6 were taking both. How many were not taking either subject?
Click here to see answer by edjones(8007)

Question 383821: In how many ways can a group of 11 elect a president, secretary, and treasurer?
Click here to see answer by edjones(8007)

Question 383824:
There are five girls and five boys at a party. In how many ways can they be seated in a row of six?
Click here to see answer by edjones(8007)

Question 383186: How many different ways can a gold, a silver, and a bronze medal be awarded to 6 runners?
Click here to see answer by sudhanshu_kmr(1152)

Question 385297: the digits 4,5,6,7,8,9 are randomly arranged to form a three-digit number. (digits are not repeated) find the probability that the number is even and greater than 900
Click here to see answer by sudhanshu_kmr(1152)

Question 385048: SEVEN HOUSES IN A ROW ARE TO BE PAINTED WITH ONE OF THE COLORS RED, BLUE, GREEN OR YELLOW. IN HOW MANY DIFFERENT WAYS CAN THE HOUSES BE PAINTED SO THAT NO TWO ADJACENT HOUSES ARE THE SAME COLOR?
Click here to see answer by sudhanshu_kmr(1152)

Question 385348: Ten fish are caught in a lake, marked, and then returned to the lake. Two days later 20 fish are again caught, 2 of which have been marked.
(a) Find the probability of 2 of the 20 fish being marked if the lake has k fish (assuming the fish are caught at random).
(b) What value of k maximizes the probability?

Click here to see answer by stanbon(75887)

Question 385347: What is the probability that 2 (or more) people in a random group of 25 people have a common birthday? (This is the famous Birthday Paradox Problem.)
Click here to see answer by sudhanshu_kmr(1152)

Question 385820: Allen is in the Boy Scouts. He has three weeks left in which to complete the hours required for a merit badge in community service. Because of his paper route and homework, he can't put in more than 5 hours in any one week for the merit badge. How many different ways can Allen work a total of 10 hours over the three week period? So far I have 23 different combinations. I am wondering if that is the total or if there is more.
Click here to see answer by scott8148(6628)

Question 386769: If nPr = 120, and nCr=20, then determine the value of 7Pr.
Click here to see answer by jim_thompson5910(35256)

Question 386769: If nPr = 120, and nCr=20, then determine the value of 7Pr.
Click here to see answer by solver91311(24713)

Question 386796: How many ways can 3 couples sit in a row in a movie theater if all couples must sit together?

Click here to see answer by robertb(5830)

Question 386772: If a term in the explansion of (x+b)^8 is (-1701x^3)/(4096), assuming b is a constant, then the exact value of b is?
Click here to see answer by robertb(5830)

Question 386793: Determine the no. of terms in the expansion (2x^2-(1/4x))^12.
I got 13, by using the binomial theorem. Is there a way that I don't need to expand till the end?
Click here to see answer by Fombitz(32388)

Question 386795: Little Lenny Leonardson has 2 red blocks, 3 blue blocks and 2 yellow blocks. in how many diff ways can he line up the blocks?
How do you know when to use permutation OR combinatorics?
Click here to see answer by sudhanshu_kmr(1152)

Question 386910: Please help us understand this Algebra homework. I do not believe the teacher really explained this in class, and my child is confused. Thank you so much.
1) How many different license plates can be made that contain 4 letters and 3 numbers if repeating is allowed, but you cannot use Q or 7?
2) Using the digits 2,4,6,7,8 only?
a) How many 4-digit numbers can be made if repeating is allowed?
b) How many 4-digit numbers can be made if no repeating is allowed?
c) If you can repeat numbers, how many 3-digit numbers are possible that are greater than 600?
d) if no repeating is allowed, how many 5-digit numbers can you make that are greater than 60,000 and also odd?

Click here to see answer by sudhanshu_kmr(1152)

Question 387020: the probability that both Barb and Bob are both on the same committee of 4 which is choosen from their class of 10 people is?
Click here to see answer by sudhanshu_kmr(1152)

Question 387019: the probability that both Barb and Bob are both on the same committee of 4 which is choosen from their class of 10 people is?
Click here to see answer by robertb(5830)

Question 387269: How many different ways can a committee of 9 be
selected from a larger organization of 20 people?
Click here to see answer by robertb(5830)

Question 387292: suppose a code is made up of three numbers followed by 2 letters if the number 0 or 1 may not used at the beginning of the code how many codes are possible
Click here to see answer by edjones(8007)

Question 387810: A ten-person club must select a president, a vice-president and a secretary treasurer. They must also select a 3 person committee. If the officers may not serve on the committee, in how many ways may both selections be made?
Assume one person cannot be assigned more than one position.
Click here to see answer by stanbon(75887)

Question 388015: i want some very difficult questions in permutations and Combinations with the solutions and explanations >>> please
Click here to see answer by mdenny(8)

Question 388090: There are 6 boys and 4 girls and a group of 5 people must be formed. How many groups are possible consisting of 2 girls and 3 boys?
Click here to see answer by edjones(8007)

Question 388089: You toss a fair 6-sided die 5 times.find the probability that a three is rolled exactly two out of the five rolls.

Click here to see answer by ewatrrr(24785)

Question 388089: You toss a fair 6-sided die 5 times.find the probability that a three is rolled exactly two out of the five rolls.

Click here to see answer by edjones(8007)

Question 388086: You toss a fair 6-sided die 5 times. Find the probability that a three is never rolled.
Click here to see answer by ewatrrr(24785)

Question 388086: You toss a fair 6-sided die 5 times. Find the probability that a three is never rolled.
Click here to see answer by solver91311(24713)

Question 388108: There are 6 boys and 4 girls and a group of 5 people must be formed. How many groups are possible consisting of 2 girls and 3 boys
Answer:
nCr=combination of n things taken r at a time= n!/((n-r)!*r!)
4C2 * 6C3
=6*20
=120 groups
If a group is chosen randomly from the 10 people, find the probability that the group will consist exactly of 2 girls and 3 boys.

Click here to see answer by Theo(13342)

Question 388175: A phone dial has 10 holes. How many different signals, each consisting of 7 impulses in succession, can be formed if:
a) no impulse is to be repeated in any given signal?
b) if repetitions are permitted?
Click here to see answer by stanbon(75887)

Question 388170: A committe of 4 is to be chosen from a group of 6 boys and 5 girls my question is what is the probability that a committee consists of exactly two boys and two girls, have atleast one girl on it, have at least one girl and at least one boy on it, have at most one girl on it?
Click here to see answer by stanbon(75887)

Question 388221: (n+1)/(n-1) write it as a factorial
I also want a help in writing any other formula as a factorial
Click here to see answer by Alan3354(69443)

Question 388463: can you answer this and I will be greatful
Ten women and their husbands are to be seated on two sides of a long rectangular table, ten on each side. How many possible seating arrangements are there if
a) all the women sit on the same side?
b) women and men alternate along the able and every women sits opposite a man?
c) everyone sits opposite of their spouse?

Click here to see answer by Edwin McCravy(20054)

Question 388594: In how many permutations of the word AUROBIND do the vowels appear in alphabetical order
Click here to see answer by robertb(5830)

Question 388457: I. Seven letter words are formed using the letters of the word BLACKER.
(a)How many which end in R? (b)How many in which E immediately follows K?
(c)How many do not begin with B?(d)How many in which the vowels are separated by exactly two letters? (e)How many in which the vowels are seperated by two or more letters?
I really appreciate any help
Click here to see answer by edjones(8007)

Question 388756: 6 people will sit in pairs on 3 benches. How many possible ways can they be arranged?
Like.
1 2 and 3 4 and 5 6 = 1 way
1 2 and 4 3 and 5 6 = 2 ways
1 2 and 3 4 and 6 5 = 3 ways
1 3 and 2 4 and 5 6 = 4 ways
Click here to see answer by Edwin McCravy(20054)

Question 388972: A sample of 4 mousetraps taken from a batch of 100 mousetraps is to be inspected. How many different samples could be selected?
Click here to see answer by haileytucki(390)

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