Question

How many different 12-member juries can be chosen from a pool of 35 people?

Answer 1

35C12 = 834,451,800
using combination

Answer 2

834451800

Explanation:

Permutation refers to arrangement of objects such that repetition is not allowed and order matters .

`n_P_r=(n!)/((n-r)!)`

Combination is all about selecting things from a group of objects such that repetition is allowed and order does not matter.

`n_C_r=(n!)/(r!(n-r)!)`

Here, we need to find how many different 12-member juries can be chosen from a pool of 35 people .

As it's about selection such that repetition is allowed and order does not matter , we will use combination.

Take n = 35 and r = 12 , we get

`\left ( 35 \right )_C_(12)=(35!)/(12!(35-12)!)\\\\=(35!)/(12!23!)\\\\=834451800`