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

Number of people in the audience = 250

     Number of volunteers required to perform the magic act from the audience =2

As 2 people can be selected from 250 people by using the properties of combination as order of choosing people is not important.

Possible number of ways = $_{2}^{250}\textrm{C}$

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

                      = 31125 ways

Answer 2

The answer should be 250 objects taken 2 at a time