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

Step-by-step 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 :

$^{n+r-1}C_r\\\\=^{5+3-1}C_{3}\\\\=^{7}C_3=\dfrac{7!}{3!(7-3)!}\ \ [\because\ ^nC_r=\dfrac{n!}{r!(n-r)!}]\\\\=\dfrac{7\times6\times5\times4!}{3\times2\times1\times4!}=35$

Hence, there are 35 variations of three scoop servings.