Question

2.Two people out of a group of 75 will win tickets to an upcoming concert. How many different groups of two are possible?

Answer 1

ANSWER

2775

EXPLANATION

We have to find how many combinations of two people are possible since order does not matter. This is because both people will win a ticket, it does not matter which one is picked first,

$_2C_{75}=\frac{75!}{2!(75-2)!}=\frac{75!}{2!\cdot73!}=\frac{75\cdot74\cdot73!}{2!\cdot73!}=\frac{75\cdot74}{2}=2775$

Hence, 2775 groups of two people are possible.