Question

A magician performing a magic act has asked for 2 volunteers from the audience to help with his routine. If there are 250 people in the audience, which of the following expressions represents the number of possible pairs of volunteers?

Answer 1

Solution:

Number of people in the audience = 250

Number of Volunteers to be chosen from 250 volunteers = 2

As this can be done by choosing 2 people out of 250 peoples , the order is not important.

So , we will use combinatorics for this method, because order does not matter here.

So Possible combination= $_{2}^{250}\textrm{C}$

  =  $\frac{250!}{248!\times 2!}=249 \times 125$

  = 31125 ways

Answer 2

The answer is 125. If you were to pair 250 people in 2, that would be 250 divided by 2. And 250 divided by 2 is 125.