Question

Which of the following expressions would give the number of 5 person committees that could be formed from a group of 20 people?

Answer 1

Answer with explanation:

Number of People in the group = 20 People

Number of people required to form a committee= 5 people

Number of ways , by which committee of 5 person can be formed from a group of 20 people

=As,order of arrangement of 5 persons is not important,they can be placed in any order ,so we will use the concept of Combinatorics

`=_(5)^(20)\textrm{C}\\\\=(20!)/((20-5)!* 5!)\\\\=(20!)/(15! * 5!)\\\\=(15! *16* 17 * 18 * 19 * 20)/(15! * 5 * 4 * 3 * 2 * 1)\\\\=(16 * 17 * 18 * 19 * 20)/(20 * 6)\\\\=16 * 17 * 3 * 19\\\\=15504`

Therefore, total number of ways of arranging 5 persons from a group of 20 person =15,504 ways

Answer 2

C(20, 5) is the expression that would give the number of 5 person committees that could be formed from a group of 20 people.

To add, a combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected.