Asap. Find the number of distinguishable permutations of the digits of the number 287,772​

60

Step-by-step explanation:

Use r-combinations.

Treat it as though u are filling in 6 slots

_ _ _ _ _ _

1. First fill in the 7s, there are three of them and 6 ways to do so

so (6 Choose 3)

2. then fill in the 2s, now with the 3 slots taken up by the 7, 3 slots left.

So its (3 Choose 2).

3. and only 1 way to fill in the 8. (1 choose 1)

By multiplicative rule,

(6C3) * (3C2) * (1C1) = 60