How many different vertical arrangements are there of 10 flags if 4 are white, 3 are blue, 2 are green and 1 is red?
I know the answer is 12 600 but am not sure how to get to it. Could someone walk me through this please?
2026-04-14 19:27:38.1776194858
How many different vertical arrangements are there of 10 flags if...?
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This is the solution.
Suppose that all of the flags (even same-colored), are distinct. Then there are 10! ways.
Now we count how many times each arrangement is repeated since same-colored flags are considered the same. 4 white flags could be done in 4! ways (if they are distinguishable). Similar for the other colors. Thus # of repetitions is $4!\cdot3!\cdot2!\cdot1!$.
Thus we divide 10! by the number of repetitions to get $\frac{10!}{4!\cdot 3!\cdot 2!\cdot 1!}=12600$.