6.2 Q-19 | Permutation, Combination And Probability | Mathematics 11

Exercise 6.2 — Question 19

How many committees of 5 members can be formed from a group of 8 people?

Note: If the original problem statement differs, replace the above with the correct text from the textbook.

The number of ways to choose $r$ items from $n$ distinct items (order does not matter) is given by:

$(r n) = \frac{n !}{r ! ( n - r )!}$

We need to select 5 members from 8 people, where order does not matter.

$(5 8) = \frac{8 !}{5 ! ( 8 - 5 )!} = \frac{8 !}{5 ! \cdot 3 !}$

Expanding:

$= \frac{8 \times 7 \times 6 \times 5 !}{5 ! \times 3 \times 2 \times 1} = \frac{8 \times 7 \times 6}{6} = \frac{336}{6} = 56$

Answer: 56 committees can be formed.

Combinations are used when the order of selection does not matter. This distinguishes them from permutations, where order is important.

$(r n) = (n - r n)$

This symmetry property means $(5 8) = (3 8) = 56$ , which can serve as a useful check.