Question

Suppose a florist is creating a bouquet with 3 different types of flowers and 3 different types of greenery. If there are 7 types of flowers in the shop and 6 types of greenery to choose from, how many ways can the florist design the bouquet?

Answer 1

Florist has to choose 3 types of flowers from 7 types of flowers so the combination is C(7,3)
and chooses 3 types of greenery from 6 types of greenery so the combination is C(6,3)
Formula for combination is:
C(n,r) = n! / r!(n-r)
C(7,3) = 7! / 3! (7-3)!
=7 x 6 x5 x4 x3 x 2/ 3 x2 (4x3x2)
=5040 / 144
= 35
Now for greenery, C(6,3) = 6! / 3! (6-3)!
= 6x5x4x3x2 / 3x2(3x2)
=720/36 = 20
So, there are 35 combinations for flowers and 20 combinations for greenery,
total combination = 35 x 20 =700