Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote the total number of one-one functions from the set A to the set A × B . Then :

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Given, n A = 3 , n B = 5 ⇒ n A × B = 15 x = C 3 5 × 3 ! = 5 × 4 × 3 = 60 y = C 3 15 × 3 ! = 15 × 14 × 13 = 30 × 91 2 y = 60 × 91 ∴ 2 y = 91 x

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