Question

There are five flavors of ice cream: C, M, B, S and V.

a) How many variations of three scoop servings are there? (order of the scoops does not matter; different scoops could be of the same flavor)

Answer 1

Answer: 35

Explanation:

Given :The number of different flavours of ice-cream are there : n= 5

The number of scoops in a serving : r = 3

If the order of the scoops does not matter and the different scoops could be of the same flavor , then we can use Combinations with repetitions.

Thus , the number of variations of three scoop servings are there will be :

`^(n+r-1)C_r\\\\=^(5+3-1)C_(3)\\\\=^(7)C_3=(7!)/(3!(7-3)!)\ \ [\because\ ^nC_r=(n!)/(r!(n-r)!)]\\\\=(7*6*5*4!)/(3*2*1*4!)=35`

Hence, there are 35 variations of three scoop servings.