Probablity word problem

Question

A florist is creating a bouquets put of red, yellow, and white roses. If there are five red roses, 4 yellow roses and eight whight roses how many different arrangements can be made using two of each color

Answer 1

We want to choose 2 of the 5 red roses, 2 of the 4 yellow roses, and 2 of the 8 white roses.

 

 

 

RED ROSES:

 

(5 choose 2) = ₅C₂ = (5!)/((2!(5-2!)) = (5×4×3×2×1)/(2×1(3!)) = (5×4×3)/(3×2×1) = (5×4)/2 = 10 ways to choose red roses

 

YELLOW ROSES:

 

(4 choose 2) = 6 ways to choose yellow roses

 

WHITE ROSES:

 

(8 choose 2) = 28 ways to choose white roses

 

 

 

10×6×28 = 1680 ways to choose the roses