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

they wear them?

2
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they wear them?

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

4!/ (3-4)!=4!/1!=1*2*3*4 /1=24 ways

Number of ways in which 3 Men can wear 5 waist coats =

5!/ (5-3)! = 5!/2!= 1*2*3*4*5 /1*2= 3*4*5=60 ways

Number of ways in which 3 Men can wear 6 caps

6! /(6-3)! = 6!/3!= 1*2*3*4*5*6/1*2*3 = 4*5*6=120 ways

Total number of ways = 24 + 60 + 120 = 204

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You have to have a idea in permutations to solve this

so 6 hats can be wore by three man in ⁶P₃ = 120

5 waistcoats can be wore by three man in ₅P₃ = 60

4 coats can be wore by three man in ⁴P₃ = 24

so no of ways is 120 + 60 + 24 = 204 ways is the answer

so 6 hats can be wore by three man in ⁶P₃ = 120

5 waistcoats can be wore by three man in ₅P₃ = 60

4 coats can be wore by three man in ⁴P₃ = 24

so no of ways is 120 + 60 + 24 = 204 ways is the answer