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

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 Question 391824: How many different signals can be made from 6 different flags if each signal is to consist of 3 flags hung in a horizontal row? Click here to see answer by sudhanshu_kmr(1152)

 Question 391826: How many sums of money, each involving 3 coins, can be formed from a penny, a nickel, a dime, and a quarter? Click here to see answer by Edwin McCravy(9719)

 Question 392048: The number of students divided equally into four teams Click here to see answer by stanbon(60778)

 Question 392151: prove that P(n,n) = 2P(n,n  2) and prove that C(2n,2) = 2C(n,2) + n^2 . Click here to see answer by robertb(4012)

 Question 392603: how many different 4-digit numbers can be formed from th digits 2, 3, 4,5,6,7,and 8 if: a)repetition of digits is not allowed? b)repetition of digits is allowed? c)how many of them are odd numbers? refer to (a). d)how many of them are even numbers? refer to (b). Click here to see answer by sudhanshu_kmr(1152)

 Question 392595: There are 3 mangoes, 4 Guava & 5 oranges.In how many ways can they be arranged in a row. Click here to see answer by sudhanshu_kmr(1152)

 Question 392402: our companys id cards consist of 3 letters followed by 2 numbers. how many cards can be made if repetitions are allowed? Click here to see answer by sudhanshu_kmr(1152)

 Question 392593: find the total no. of numbers less then 1000 & divisible by 5 that can be formed with the digits 0,1,2,3,4,5,6,7,8,9(none of the digits repeated). Click here to see answer by sudhanshu_kmr(1152)

 Question 392597: In how many ways can the letters of the word ALLAHABAD be arranged so that the vowels can occupy only even positions. Click here to see answer by sudhanshu_kmr(1152)

 Question 392653: I will have four guests for bridge, for a total of five players. We play four hands and then rotate partners. One will sit out in each round. Is there a combination which would have all players to play the same number of rounds; if so, how many rounds would be required? Click here to see answer by solver91311(18785)

 Question 393118: There are 3 people who are chosen to serve on a committee out of a group of 3 girls and 4 boys. How many different committees can be formed? Click here to see answer by ewatrrr(11176)

 Question 393195: How many different ways are there to seat 20 people in 20 different seats? Click here to see answer by MathLover1(7480)

 Question 393530: Suppose we flip four coins simultaneously: a penny, a nickel, a dime, and a quarter. What is the probability that (a) they all come up heads? (b) the penny and nickel both come up heads? (c) the penny and dime both come up the same? (d) at least 15 cents wort of coins come up heads? Click here to see answer by stanbon(60778)

 Question 393533: 3 cards are chosen at random from a standard 52-card deck. What is the probability that they form a pair? (A 3-card hand is a pair if two of the cards match in rand but the third card is different.) Click here to see answer by stanbon(60778)

 Question 393532: Suppose 5 different integers are randomly chosen from between 20 and 69, inclusive. What is the probability that they each have a different tens digit? Click here to see answer by edjones(7794)
 Question 393532: Suppose 5 different integers are randomly chosen from between 20 and 69, inclusive. What is the probability that they each have a different tens digit? Click here to see answer by richard1234(5390)

 Question 393531: Suppose two distinct integers are chosen from between 5 and 17, inclusive. What is the probability that their product is odd? Click here to see answer by solver91311(18785)
 Question 393531: Suppose two distinct integers are chosen from between 5 and 17, inclusive. What is the probability that their product is odd? Click here to see answer by sudhanshu_kmr(1152)

 Question 393607: in how many different ways can a true-false test containing of 9 questions be answered? Click here to see answer by robertb(4012)

 Question 394013: n coins are simultaneously flipped. The probability that at most one of them shows tails is 3/16. Find n. Click here to see answer by robertb(4012)

 Question 394012: 8 coins are simultaneously flipped. What is the probability that heads are showing on at most 2 of them? Click here to see answer by robertb(4012)

 Question 394011: A bag has 3 red and k white marbles, where k is an (unknown) positive integer. Two of the marbles are chosen at random from the bag. If the probability that the two marbles are the same color is 1/2, find k. Click here to see answer by robertb(4012)

 Question 394009: One member of the debate team is going to be chosen President. Each member is equally likely to be chosen. The probability that a boy is chosen is 3/4 the probability that a girl is chosen. Girls make up what fraction of the debate team? Click here to see answer by robertb(4012)

 Question 394463: The letters of the word "SIXTEEN" are randomly arranged. What is the probability that the two E's are not next to each other? Click here to see answer by robertb(4012)

 Question 394477: 15. Lara has been invited to a picnic on Saturday. The picnic will occur, rain of shine. If it rains, there is a 20% probability that Lara will decide to go, but if it's sunny, there is an 80% chance of rain. What is the probability that Lara will attend the picnic? 16. Three cards are dealt at random from a standard deck of 52 cards. What is the probability that: (a) The first card is a Jack, the second card is a Queen, and the third card is a King? (b) All three cards are hearts? (c) The first card is a 4, the second card is a club, and the third card is a 2? Click here to see answer by edjones(7794)

 Question 394470: A standard deck of 52 cards is shuffled. What is the probability that (a) the top card is a heart? (b) the top card is a 5? (c) the top card is the King of diamonds? (d) the top card is a face card? (e) the top card red and the second card is black? (f) the top card is a 3 and the second card is an 8? (g) the top two cards are Aces? (h) the top three cards are Spades? Click here to see answer by pie90010(44)

 Question 394730: There are 5 groups (A,B,C,D,E)and in each group there are 4 teams. Each team in a group will play against the other team only once. how many games will each group play? How many games are played total? Click here to see answer by MCAT(6)

 Question 394474: Spiffy the Spider has 8 legs, each of which is a different color. Spiffy has a sock and a shoe for each of his eight legs (so that he has one sock and one shoe in each of the eight colors). In how many ways can Spiffy put on his socks and shoes, if each sock and shoe must go on with the matching color, and the sock must go on before the shoe? Click here to see answer by richard1234(5390)

 Question 394740: Let (x) = 3x2  2x and g(x) = x  6. Find each value. show me step by step please:) (  g)(2) Click here to see answer by robertb(4012)

 Question 395385: Sarah decided to try telemarketing. She calls people from 3pm to 9pm. Marley has a 15% chance of being called during this time. If Marley eats dinner from 6:6:30, how likely is it that she'll have a conversation with Sarah during this time? Click here to see answer by jrfrunner(365)

 Question 395641: Suppose that two fair dice are tossed. What is the probability that the sum is an even number given that it exceeds 9 Click here to see answer by Edwin McCravy(9719)

 Question 395702: When throwing a pair of dice, find the probability that the numbers shown have a difference of 3. Click here to see answer by ewatrrr(11176)

 Question 395917: there are several routes for denzell to ride his bike. he says he can travel a different way every weekend for 52 weekends never repeating the same journey is he correct, explain please i am stumped thank you for your time Click here to see answer by richard1234(5390)

 Question 395700: How many ways can you arrange 5 employees in a circular table with only three seats? Click here to see answer by sudhanshu_kmr(1152)

 Question 396177: A group consisting of 3 boys and 2 girls is to line-up in a row for a photograph. In how many ways may this be done assuming that (a) there are no restrictions? (b) the boys and the girls are each to stand together? (c) only the two girls are to stand together? (d) Rachel and Jonathan must not stand together? Click here to see answer by sudhanshu_kmr(1152)

 Question 396688: 1. how many different ways can the letters "SIMILAR" be arranged if letter "I" must be first letter? 2. how many different ways can the letters "TRIGONOMETRY" be arranged if a vowel must be first letter? Click here to see answer by sudhanshu_kmr(1152)

 Question 396791: If 5 students are all sitting in a row of seats, In how many different ways can they seat themselves? Click here to see answer by ewatrrr(11176)

 Question 396795: a 4-letter word is to made using letters from the set (a,b,c,d,e,f) How many words are possible assuming that a)there are no restrictions b) no repetition of letters is permitted c) adjacent letters in the word may not be the same? Click here to see answer by sudhanshu_kmr(1152)

 Question 396981: in how many ways can the letters of the word today be arranged using only 3 of the letters at a time Click here to see answer by Alan3354(34679)

 Question 396609: if 4 letters of the word "MATHEMATICAL" are ramdomly selected,how many combinations can be found? How many permutations can be found of the 4 letters selected? Click here to see answer by Edwin McCravy(9719)

 Question 397991: A baseball manager chooses his lineup 1-9. How many ways can he organize his lineup if the pitcher doe not hit in the first four? I did 9*8*7*6*6*5*4*3*2 is this correct? Click here to see answer by josmiceli(10616)
 Question 397991: A baseball manager chooses his lineup 1-9. How many ways can he organize his lineup if the pitcher doe not hit in the first four? I did 9*8*7*6*6*5*4*3*2 is this correct? Click here to see answer by stanbon(60778)

 Question 397989: What is the probability that if you rearranged the letters in the word TURKEY, you would get a word that starts with R and ends with a vowel? I tried two ways to get the answer and I don't know which is correct. 1) (1/6) * (2/5) = 1/15 2) ((C (6.1) * C(5.2)) / 6! = 1/12 Are either of these correct? Click here to see answer by stanbon(60778)

 Question 397990: 3A store has 5 shirts, 4 Jackets, 8 Pants, and 2 Socks. In how many ways (different orders) can these objects be put on display? ( Jacket, Jacket is the same as Jacket, Jacket. I.E treat all the items of the same object as the same) I tried (21!/(5!*4!*8!*2!) Is this correct? Click here to see answer by richard1234(5390)

 Question 398094: the letters in the word BANANAS are to be arranged.A word can be considered formed without being meaningful.Finds event R, Q and T. R: the words start and end with an A Q: All the N's in the word are kept together T: All the A's in the word are kept together Click here to see answer by stanbon(60778)