We are building a snowman! How many different ways can 3 buttons and 2 stick arms be chosen from 15 buttons and 6 sticks

Question

This is a probability word problem. it is asking a combination/ permutation question

Answer 1

15C3 times 6C2

nCr=n!/r!(n-r)!

15!/3!(12!)=(15*14*13)/(3*2*1)=5*7*13=455 ways

6!/2!(4!)=(6*5)/(2*1)=15 ways

455*15=6825 ways