Exercise 6.2 — Question 7

Problem

This question involves applying the combination formula to count selections. A combination is used when the order of selection does not matter.

The number of ways to choose $r$ items from $n$ distinct items is:

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

Note: Insert the specific problem statement for Exercise 6.2 Q7 from the FBISE textbook here.

Identify the total number of items $n$ and the number to be selected $r$ .
Check whether any conditions apply (e.g., certain items must be included or excluded).
Apply the combination formula $(r n) = \frac{n !}{r ! ( n - r )!}$ .
Simplify the factorials step by step.

How many ways can a committee of 3 be chosen from 8 people?

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

So there are 56 ways.

This question involves applying the combination formula to count selections. A combination is used when the order of selection does not matter.

The number of ways to choose $r$ items from $n$ distinct items is:

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

Note: Insert the specific problem statement for Exercise 6.2 Q7 from the FBISE textbook here.

Identify the total number of items $n$ and the number to be selected $r$ .
Check whether any conditions apply (e.g., certain items must be included or excluded).
Apply the combination formula $(r n) = \frac{n !}{r ! ( n - r )!}$ .
Simplify the factorials step by step.

How many ways can a committee of 3 be chosen from 8 people?

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

So there are 56 ways.