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?

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