Find number of variants.For 5 flavors of ice cream you can have 3 scoops. How many variants are available. Use combinations.

We have 5 flavors of ice cream and we can take 3 scoops in
each or which can be any of the flavors.

Now as we get the
same variant whether we take the 1st flavor first or take the first flavor last, so our
order of choosing flavors does not matter. We are only interested in finding the total
number of combinations, not the total number of
permutation.

Now the formula for filling 3 slots, each with
one of the 5 flavors is given by C (n + r -1, r) = [(n+r-1)!] /
[r!*(n-1)!]

Here n is 5 and r is
3.

Therefore C (n + r -1, r) = [(n+r-1)!] /
[r!*(n-1)!]

=> [5 + 3 - 1)! ] /
[3!*(5-1)!]

=> 7! / ( 3! *
4!)

=> 7*6*5/
3*2

=> 7*5

=>
35

The number of variants possible is
35.