Ben wants to buy a new collar for each of his 3 dogs . The collars come in a choice of 6 different colors .
Step1 : How many selections of collars for 3 dogs are possible if repetitions of colors are allowed.
In this problem
we have a combinations with repetitions allowed
so
the formula is equal to
nCr=(r+n-1)!/[r!(n-1)!]
we have
n=6
r=3
substitute
6C3=(3+6-1)!/[3!(6-1)!]
6C3=8!/[3!*5!]=(8*7*6)/(3*2*1)=56
