Question

Three men have 4 coats, 5 waistcoats and 6 caps. In how many ways can
they wear them?

Answer 1

A n K = n!/ (N-k)!

Number of ways in which 3 Men can wear 4 coats = 
4!/ (3-4)!=4!/1!=1*2*3*4 /1=24 ways


Number of ways in which 3 Men can wear 5 waist coats =
5!/ (5-3)! = 5!/2!= 1*2*3*4*5 /1*2= 3*4*5=60 ways


Number of ways in which 3 Men can wear 6 caps
6! /(6-3)! = 6!/3!= 1*2*3*4*5*6/1*2*3 = 4*5*6=120 ways


Total number of ways = 24 + 60 + 120 = 204

Answer 2

you have to have a idea in permutations to solve this
so 6 hats can be wore by three man in ⁶P₃ = 120 
    5 waistcoats can be wore by three man in ₅P₃ = 60
 4 coats can be wore by three man in ⁴P₃ = 24
so no of ways is 120 + 60 + 24 = 204 ways is the answer