Question

How many different 12 member juries can be chosen from a pool of 25 people?

Answer 1

Answer: 5200300

Step-by-step explanation:

Given: Total number of people = 25

The number of  member juries can be chosen from a pool of 25 people= 12

To calculate combinations, we use the formula as :-

$^nC_r = \dfrac{n!}{r!(n-r)!}$, where n represents the total number of items, and r represents the number of things being chosen at a time.

Now, the number of different 12 member juries can be chosen from a pool of 25 people is given by :_

$^{25}C_{12} = \dfrac{25!}{12!(25-12)!}\\\\=\dfrac{25!}{12!13!}=5200300$

Hence, the number of different 12 member juries can be chosen from a pool of 25 people is 5200300.

Answer 2

A formula for the number of possible combinations or r objects from a set of n objects is 
$nCr = \frac{n!}{r!(n-r)!}$
where n is 25 and r is 12. The number of ways is 5,200,300.