Question

When preparing a bouquet, a florist can choose from seven roses, six carnations, and four chrysanthemums. How many bouquets can the florist make if the bouquet must have at least one flower?

Answer 1

The possible numbers of roses are 0,1,2,3,4,5,6,7.

The possible numbers of carnations are 0,1,2,3,4,5,6.

The possible numbers of chrysanthemums are 0,1,2,3,4.

Bur the combination 0 roses, and 0 carnations, and 0 chrysanthemums is impossible.

Then the total number of  bouquets is

$$8(7)(5)-1=279$$