John has 7 bananas and 3 kiwis. In how many ways can John divide the 1

Solution:

Since there are 3 different kiwis and since each parcel must contain at least one kiwi, one of the parcels will get 2 kiwis and the other parcel will get 1 kiwi. Let’s calculate the number of ways to form the parcel containing 2 kiwis.

We can choose 2 kiwis out of 3 kiwis in 3C2 = 3 ways. Since each parcel is required to contain 5 pieces of fruit, we must choose 3 bananas from a total of 7 bananas. This choice can be made in 7C3 = 7!/(3!*4!) = (7 x 6 x 5)/(3 x 2) = 35 ways. Thus, there are 3 x 35 = 105 ways to form this parcel. Since the other parcel will get all the remaining fruit, the number of ways to divide the fruit into two parcels is also 105.

Notice that we would obtain the same result if we calculated the number of ways to form the parcel containing 1 kiwi (since we would calculate 3C1 x 7C4 = 3 x 35 = 105).

Answer: D