Waist Coats, Coats and Caps

Probability Level 4

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


The answer is 172800.

Prakriti Bansal by prakriti bansal , 23, China

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1 solution

Tushar Verma
Sep 26, 2014

Selection of clothes for three boys = 4C3 * 5C3 * 6C3=2400.

3 different coats can be used by 3 boys in 3! ways.

Same will be applied for waist coat and caps too.

So, 3! * 3! * 3! = 216, but one particular combination will be repeated for each boy.

total different combination for above selection = 216/3 = 72

hence total no of ways = 2400*72 = 172800

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Can you explain what you mean by "one particular combination will be repeated for each boy"? In what sense is it repeated, or are the boys considered identical?

A much better way of thinking about it is to look at permutations directly.

Calvin Lin Staff - 6 years, 6 months ago

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