Question

Three Men have $4$ coats $5$ waist Coats, and $6$ caps. The number of ways they can wear them is

• A. ${}^1{}^5{P}_3$
• B. $4^3{5}^3{6}^3$
• C. ${}^4{P}_3{}^5{P}_3{}^6{P}_3$
• D. $180$

Answer 1

The correct option is C ${}^4{P}_3{}^5{P}_3{}^6{P}_3$

Coats ${\to }^4{P}_3$

4

3

2

Waist Coats ${\to }^5{P}_3$

5

4

3

Caps ${\to }^6{P}_3$

6

5

4

Total no. of ways of wearing them= ${}^4{P}_3$ x ${}^5{P}_3$ x ${}^6{P}_3$