A class has 7 recitation sections. 3 of the recitation sections are led by a pair of TAs, and 4 recitation sections are led by a trio of TAs. There are also 2 TAs who do not teach recitation. How many ways are there to line up all of the TAs such that each TA with a recitation partner(s) is standing next to them? How many 8 digit strings contain the digit 5 exactly once, the digit 2 exactly twice, and the digit 7 exactly thrice? Leading Os are allowed.

Q: How many arrangements are there of the letters of the word MATHEMATICS in which all the vowels…

A:

Q: There are 17 students in a class, and 5 of them will be chosen to go on a field trip. How many ways…

A: The objective of this question is to find out the number of ways in which 5 students can be chosen…

Q: Among 10 students , 4 of them will be selected for a project .in how many ways can they be selectes

A: In question, We have given that among 10 students , 4 of them will be selected for a project. The…

Q: How many outfits can be made from 4 pairs of slacks, 5 shirts, and 3 ties, if one selection from…

A: First decide on a pair of slacks.For that there are 4 different choices.Now for each of those…

Q: How many different 4-letter radio-station call letters can be made   if the first letter cannot be…

A: Given: 4- letter radio-station call letter has to be made with first letter should not be A, B or C…

Q: How many arrangements can be made from the letters of the word

A: Given, the word                   GODDESS

Q: You can answer any 19 questions from the 21 questions on an exam. In how many different ways can you…

A: Here it is given that the order is of no importance, we will use the combination rule here where we…

Q: |(a) How many ways can this be done, if the order of the choices matters? (b) How many ways can this…

A: Letters - A,B,C n= 3 r = 2

Q: How many ways can 6 ladies be seated in a circular table such that 2 of the ladies must always sit…

A: To find: The number of ways to arrange 6 ladies in a circular table such that 2 of the ladies must…

Q: A team composed of two grade 11 and two grade 10 students is to be sent to a debate contest. If…

A: The provided information is  There are Two grade 11 and two grade 10 students  There are also 60…

Q: A photographer wishes to arrange 7 children consisting of 3 boys and 4 girls in a straight line for…

A:

Q: My first car had a license plate which had 3 letters followed by 3 digits. How many different such…

A: We have to find different licenses plates.

Q: How many ways can 4 books be arranged on a shelf if the books are selected from a collection of 100…

A: Here we will use the concept of permutation Permutation = nPr = n!/(n-r)!

Q: Suppose that 4 Pistons need to be installed in a new engine block. there is a production run of 100…

A: Given, there is a production run of 100 Pistonsand 4 Pistons need to be installed in a new engine…

Q: 2. Let = = 4cjs49°, = 2/2cjs92°, and , = cjs (-86°). Evaluate the expression ち+(-)

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Q: How many ways to arrange 5 books on the shelf exist if two definite books are not placed together.

A:

Q: Four married couples have bought 8 seats in the same row for a concert. In how many diff ways can…

A: Given: Four married couples have bought 8 seats in the same row for a concert.

Q: An instructor gets 5 calls in 3 hours. a. How likely is it that the teacher will get exactly 10…

A:

Q: Consider the number of different ways in which 3 flags can be displayed on a flagpole, one above the…

A: I am going to solve the problem by using some simple geometry to get the required result of the…

Q: How many 15 letter strings containing only a's, b's, and c's have 6 a's and 4 b's?

A: Given: 15 letter strings containing only a's, b's and c's

Q: 10. There are 11 women and 9 men in the math department. (a) How many ways can a committee of 4…

A: The combination rule of counting is used when the order of selection does not matter. So the number…

Q: Out of 800 families with 5 children each how many would you expec to have i) 3 boys (ii ) either 2…

A: Given: Total number of families=800Number of children=n=5

Q: Find the number of arrangements of the letters in the word EMERGE in which (a) all the 3 letters E…

A: Given word is EMERGEletter E is repeated 3 times total no.of letters in the word  EMERGE  =6

Q: how many five letter codes can be made if each chosen letter (from the the original 7 letters) can…

A:

Q: Find the amount of money owed at the end of 5 years if $60,000 is borrowed at 7% per year compounded…

A: Here we have to find amount of money at the end of 5 years if money borrowed is $60, 000 at 7% rate…

Q: Suppose that there is a bag containing 6 marbles. How many ways can you draw 4 marbles from the bag…

A: The bag contains =6 marbles number of marbles drawn=4

Q: There are 24 books on a shelf. How many ways are there to choose 10 of them so that no two of the…

A:

Q: A computer user has downloaded 23 songs using an online file-sharing program and wants to create a…

A: GivenNo.of downloaded songs(n)=23no.of  songs to use in CD player(r)=8

Q: How many seven-digit numbers can be made from the digits 1 to 9 if repetition is allowed?

A: Given that  To find the number of ways of 7 digit number can be made from the 1 to 9

Q: Find in how many ways you can distribute 8 different gifts to 3 people so that everyone gets at…

A: Step 1: Step 2: Step 3:

Q: A bell rings every 2 seconds, and a bird chirps every 3 seconds. If the ring and the chirp occur…

A: A bell rings every 2 seconds, and a bird chirps every 3 seconds.If the ring and the chirp occur…