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Question

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

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Solution

4 coats

5 waistcoats

6 caps

Number of ways in which 3 Men can wear 4 coats =

4!(34)! =4!1! =1×2×3×41=24 ways


Number of ways in which 3 Men can wear 5 waistcoats =

5!(53)! =5!2! =1×2×3×4×51×2 =3×4×5=60 ways


Number of ways in which 3 Men can wear 6 caps

6!(63)! =6!3! =1×2×3×4×5×61×2×3 =4×5×6=120 ways


Total number of ways =24 × 60 × 120 =172800



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