Question

1. The flower shop has ten different flower arrangements. How many different ways can the shop show flowers if their display case can hold three flower arrangements and no flower arrangement is repeated?

Answer 1

We can figure out the flower combinations by choosing 1 from the set and thereby reducing the offerings available for each of three selections.

Number of ways to choose a set of 3 flower arrangements from among 10 flower arrangements will be

Having chosen 1 of these sets of 3 arrangements, number of ways to select a second set of 3 flower arrangements from among remaining 7 flower arrangements will be

Having chosen the second set of 3 flower arrangements, number of ways to select a third set of 3 flower arrangements from among 4 remaining flower arrangements will be

At the end we are  left with a single flower arrangement not chosen to display.

Hence number of ways the shop can show flowers if their display case can hold three flower arrangements and no flower arrangement is repeated will be