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Question
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
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Solution
Number of men = 3
Number of coats = 4
Number of waist coats = 5
Number of caps = 6
4 coats can be given to 3 men in 4P3 ways.
5 waist coats can be given to 3 men in 5P3 ways.
6 caps can be given to 3 men in 6P3 ways.
∴ Total number of ways of wearing 3 coats, 4 waist coats and 6 caps is
= 4P3 × 5P3 × 6P3
= `(4)/((4 - 3)!) xx (5!)/((5 - 3)!) xx (6!)/((6 - 3)!)`
= `(4!)/(1!) xx (5!)/(2!)xx (6!)/(3!)`
= `(4 xx 3 xx 2 xx 1)/1 xx (5 xx 4 xx 3 xx 2 xx 1)/(2 xx 1) xx (6 xx 5 xx 4 xx 3!)/(3!)`
= 24 × 6 × 120
= 1,72,800
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