Question

Alice wants to make a fruit salad using 10 pieces of fruit. She can buy three types of fruits at the supermarket: Apples (A), Bananas (B), and Cranberries (C). She can take as many of each type of fruit as she wants but she can only have 10 in the end. One possible fruit salad can be made of 5 apples, 3 Bananas, and 2 Cranberries. (a) How many types of fruit salads can Alice make? (b) Given that she wants at least two types of fruits in the salad, how many types of fruit salads can Alice make?

Answer 1

A) 55

B) 52

Explanation:

For a= number of apples , we can choose b=10-a bananas , then the number of cranberries is fixed depending on the number of a and b

then:

Number of combinations = sum of 10-a +1= 11 -a from a=0 to 10 = 11*10 - 10*11/2 = = 55

B) If there should be at least 2 types of fruit then

Combinations = Total number - combinations with 1 fruit = 55 - 3 = 52