Question

1) Your mom sends you to the grocery store to pick up some fruit for your family. Since your family like variety, you need to pick 4 fruits so that you get 4 lbs of the first fruit, 3 lbs of the second fruit, 2 lbs of the third fruit, and finally 1 lb of the fourth fruit. If the grocery store has 30 different types of fruits, how many combinations of fruit can you bring home? Show the setup (is it a combination or permutation or something else), but the work does not need to be shown.

2) The HR team at a company takes turns planning the various parties they have. There are 25 employees in the HR team and for parties they usually pick a group of 4 to plan them.How many different teams of 4 are possible from the 25 person HR team? Show the setup(is it a combination or permutation or something else), but the work does not need to be shown.

Answer 1

1) As we are selecting 4 fruits here, but the weight of each of the 4 fruits selected is also different, therefore this is like selecting 4 fruits from 30 fruits but also arranging them in decreasing order of weight bought for them. Therefore the number of ways to do so here is computed as the permutation of 30 items taken 4 at a time. This is computed using the permutation operator here as:

2) The number of ways to choose 4 from the 25 HT team is computed here ysing the combination operator. (There is no differentiation done here on the 4 selected )