6 bananas are to be selected from a group of 8. In how many ways can this be done?

Solution:

We have to select 6 bananas from a group of 8. We have to find in how many ways it can be done.

Here there are 8 ways to choose the first non-selected banana and for each, there are 7 ways to choose the second non-selected banana.

8 × 7 = 56 of choosing a first and second banana to not be selected.

Because of this double count, the choice of choosing banana P first and banana Q second has the same effect of choosing banana Q first and banana P second.

The actual number of ways of doing it is (8 × 7)/2 = 56/2 = 28

Therefore, it can be done in 28 ways.

Aliter:

Using the ⁿc_r formula = ⁸C₆ ways = 8 !/(6! 2!)

= (8× 7 ×6×5×4×3×2)/(6×5×4×3×2 x2)

⇒ (8 × 7)/2 = 56/2 = 28

Therefore, it can be done in 28 ways.

6 bananas are to be selected from a group of 8. In how many ways can this be done?

Summary:

6 bananas are to be selected from a group of 8. It can be done in 28 ways.