3 bananas are to be selected from a group of 9. In how many ways can this be done?

Solution:

We can use combination formula to find the required number of ways.

It is given that

3 bananas are to be selected from a group of 9.

We know that formula,

ⁿC_x = n! / x! (n - x)! 

Then, if 3 bananas are to be selected from a group of 9, then the number of ways will be,

⁹C₃ = 9! / (3! (9 - 3)!)

⁹C₃ = (9 × 8 × 7 × 6!)/((3 × 2 × 1)6!)

⁹C₃ = (9 × 8 × 7 × 6!)/((6 × 6!)

⁹C₃ = (9 × 8 × 7)/6

⁹C₃ = 504/6

⁹C₃ = 84

Therefore, this can be done in 84 ways.

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3 bananas are to be selected from a group of 9. In how many ways can this be done?

Summary:

3 bananas are to be selected from a group of 9, this can be done in 84 ways.