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

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प्रश्न

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

योग
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उत्तर

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 × 6P

= `(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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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 4: Combinatorics and Mathematical Induction - Exercise 4.2 [पृष्ठ १७७]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
अध्याय 4 Combinatorics and Mathematical Induction
Exercise 4.2 | Q 3. (ii) | पृष्ठ १७७

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