Question

How many combinations of brands of pop can be made from Coke, Pepsi, Dr Pepper, and Mountain Dew when someone chooses 13 pops and it includes at least 2 Cokes and exactly 2 Pepsis?

Answer 1

Total different brands available = 4

Total pops to be chosen = 13

Overall total combinations possible = 4^13

Combinations in which we choose exactly 2 pepsis = ¹³C₂*(3^11)

Combinations in which we choose 0 cokes and exactly 2 pepsis = ¹³C₂*(2^11)

Combinations in which we choose 1 coke and exactly 2 pepsis = ¹³C₂*¹¹C₁*(2^10)

So,

Combinations in which we choose atleast 2 cokes and exactly 2 pepsis =

Combinations in which we choose exactly 2 pepsis - ( Combinations in which we choose 1 coke and exactly 2

pepsis + Combinations in which we choose 1 coke and exactly 2 pepsis) = ¹³C₂*(3^11) - (¹³C₂*(2^11) + ¹³C₂*¹¹C₁*

(2^10)) = 12779130