Question

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

• A. $172800$
• B. $172805$
• C. $172806$
• D. None of these

Answer 1

The correct option is A $172800$

The total number of ways, in which three man can wear $4$ coats, is the number of arrangements of $4$ different coats taken $3$ at a time i.e., ${}^4{P}_3$ ways.
Similarly, $5$ waist coats and $6$ caps can be worn by three men in ${}^5{P}_3$ and ${}^6{P}_3$ ways.
$\therefore$ By fundamental principle of counting
$={}^4{P}_3{\times }^5{P}_3{\times }^6{P}_3$
$=(4\times 3\times 2)\times (5\times 4\times 3)\times (6\times 5\times 4)$
$=24\times 60\times 120=172800$.