Questions
The number of ways of choosing m coupons out of an unlimited number of coupons bearing the letters A, B and C so that they cannot be used to spell the word BAC, is
detailed solution
Correct option is A
The word BAC cannot be spelt if the m selected coupons do not contain atleast one of A, B and C.Number of ways of selecting m coupons which are A or B = 2m.This also includes the case when all the m coupons are A or all are B.Number of ways of selecting m coupons which are B or C = 2m.This also includes the case when all the m coupons are B or all are C.Number of ways of selecting m coupons which are C or A = 2m.This also includes the case when all the m coupons are C or all are A.Number of ways of selecting m coupons when all are A = 1m.Number of ways of selecting m coupons when all are B = 1m.Number of ways of selecting m coupons when all are C = 1m.∴ Required number = 2m + 2m + 2m – (1m + 1m + 1m) = 3 ⋅ 2m – 3 ⋅ 1m = 3 (2m – 1).Similar Questions
Let be a set containing elements. The number of reflexive relations that can be defined on is
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