Question

There are 17 men in a choir. The choir is going to sing at a concert. Two of the men are to be chosen to make a pair to sing one of the songs. Ben thinks the number of different pairs that can be chosen is 136. Mark thinks the number of different pairs that can be chosen is 272. Who is correct, Ben or Mark? Give a reason for your answer.

A) Ben is correct; there are 136 ways.
B) Mark is correct; there are 272 ways.
C) Both are correct; there are 408 ways.
D) Neither is correct; the number of pairs is different.

Answer 1

Ben is correct; there are 136 ways. Option A

Step-by-step explanation:

In this question, we have 17 men in a choir and we need to select 2 of them to form a pair. To determine the number of different pairs that can be chosen, we can use the combination formula.

The formula for calculating combinations is nCr = n! / r!(n-r)!, where n is the total number of items and r is the number of items to be selected from the total.

Using this formula, we can calculate the number of different pairs:

nCr = 17C2 = 17! / 2!(17-2)! = 17! / 2!15! = (17 * 16) / (2 * 1) = 136

Therefore, Ben is correct. The number of different pairs that can be chosen is indeed 136. Option A.