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.
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
[tex]=_{5}^{20}\textrm{C}\\\\=\frac{20!}{(20-5)!\times 5!}\\\\=\frac{20!}{15! \times 5!}\\\\=\frac{15! \times16\times 17 \times 18 \times 19 \times 20}{15! \times 5 \times 4 \times 3 \times 2 \times 1}\\\\=\frac{16 \times 17 \times 18 \times 19 \times 20}{20 \times 6}\\\\=16 \times 17 \times 3 \times 19\\\\=15504[/tex]
Therefore, total number of ways of arranging 5 persons from a group of 20 person =15,504 ways
