Permutation Problem involving repetitions in the number of things to be chosen from and the number of slots being unequal to the number of things

24 Views Asked by At

Problem: A person has one white, two red, and three green flags. How many different signals can they make, each containing four flags arranged one above the other?

My attempt:

We have 4 slots and 6 things to choose from. But among the 6 things, there are repetitions. I know how to account for repetitions when there are same number of things to choose from as the number of slots: no. of permutations is $$ = \frac{n!}{p! \times q! \times r!}$$ [given that there are p number of repetitions of first kind, q number of repetitions for second kind, and r number of repetitions for third kind]. How can I account for repetitions in this case?