Question

Three men have four coats, five waist coats and six caps. In how many
ways can they wear them?​

Answer 1

Number of ways in which 3 men can wear 4 coats = P(4,3)=4!

So , total number of ways to wear these clothes = Product of all the above RHS terms which gives the answer 172800.

OR

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 waistcoats =

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 =172800