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

Answer» Total number of ways in which 3 men can wear 4 coats
= number of arrangements of 4 coats taking 3 at a time
= ` ""^(4)P_(3)=(4xx3xx2) =24.`
Total number of ways in which 3 men can wear 6 waistcoats
= number of arrangements of 6 waistcoats taking 3 at a time
= ` ""^(6)P_(3) =(6xx5xx4) =120.`
Total number of ways in which 3 men can wear 5 caps
= ` ""^(5)P_(3) =(5xx4xx3)=60.`
Hence, by the fundamental principal of multiplication, the required number of ways = `(24xx120xx60)` = 172800.


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