In how many ways can we partition a 15element set into three

In how many ways can we partition a 15-element set into three parts if one part has 7 elements and another part has 5 elements?

Solution

we have to make 3 parts.its given that two parts have elements 7 and 5 respectively.

so, the third part will have 15-7-5= 3 elements

in how many ways the partion can be done- 15! / 7!* 5! * 3! = 360360

ans- the partion can be done in 360360 ways