The number of ways three different natural numbers can be drawn from the set 1,2 , 3,4 , … , 10 , if minimum of the chosen numbers is smaller than 4 , is

Question

The number of ways three different natural numbers can be drawn from the set 1,2 , 3,4 , … , 10 , if minimum of the chosen numbers is smaller than 4 , is,

MARKS App · Accepted Answer

The selection must have atleast one element of the set 1,2 , 3 i.e. the required number of ways = C 1 3 ⋅ C 2 7 + C 2 3 ⋅ C 1 7 + C 3 3 ⋅ C 0 7 = 63 + 21 + 1 = 85

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