How many different ways can you select 3 bananas from a group of 9?

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To find the number of ways to select 3 bananas from a group of 9, we can use the concept of combinations. The formula for combinations is given by:

C(n, r) = n! / [r! * (n – r)!]

Where:

  • C(n, r) = number of combinations
  • n = total number of items to choose from
  • r = number of items to choose
  • ! = factorial, which is the product of all positive integers up to that number

In our case, we have:

  • n = 9 (the total number of bananas)
  • r = 3 (the number of bananas we want to select)

Now, we can substitute these values into the combinations formula:

C(9, 3) = 9! / [3! * (9 – 3)!]

This simplifies to:

C(9, 3) = 9! / [3! * 6!] = (9 × 8 × 7) / (3 × 2 × 1)

Calculating this:

  • 9 × 8 × 7 = 504
  • 3 × 2 × 1 = 6

Now, we divide:

504 / 6 = 84

So, there are 84 different ways to select 3 bananas from a group of 9. This calculation shows how combinations allow us to find the number of ways to choose items without regard to the order in which they are selected, making it ideal for this scenario.

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