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You want to buy 8 pieces of fruit from the fruit shop.The fruits you like are apples, oranges, and pears.How many different combinations are possible in your purchase if you do not necessarily have to get all of your favourites.

Question

You want to buy 8 pieces of fruit from the fruit shop.The fruits you like are apples, oranges, and pears.How many different combinations are possible in your purchase if you do not necessarily have to get all of your favourites.

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Solution

This problem can be solved using the concept of combinations with repetition.

In this case, you are choosing 8 pieces of fruit (with repetition allowed) from 3 different types (apples, oranges, and pears).

The formula for combinations with repetition is:

C(n + r - 1, r)

where n is the number of types of fruits and r is the number of fruits you want to buy.

Step 1: Substitute the given values into the formula

Here, n = 3 (apples, oranges, and pears) and r = 8 (the number of fruits you want to buy).

So, the formula becomes:

C(3 + 8 - 1, 8) = C(10, 8)

Step 2: Calculate the combination

C(10, 8) = 10! / [(10 - 8)! * 8!] = 45

So, there are 45 different combinations possible in your purchase if you do not necessarily have to get all of your favourites.

This problem has been solved

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