6.2 Q-21 | Permutation, Combination And Probability | Mathematics 11

Exercise 6.2 — Question 21

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

Note: If the original Q21 differs from the above, replace with the actual problem statement from the FBISE textbook.

The number of ways to choose $r$ items from $n$ distinct items (without regard to order) is given by the combination formula:

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

We need to choose 5 members from 8 persons.

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

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

Answer: 56 committees can be formed.

Use combinations when the order does not matter (e.g., selecting a committee).
Use permutations when the order matters (e.g., arranging people in seats).
Relationship: $^{n} P_{r} = r! \times^{n} C_{r}$