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The total number of injective mappings from a set with m elements to a set with n elements m ≤ n is equal to :(a) mn (b) nn(c) (n !/n-m) !(d) n ! |
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Answer» Correct option n ! /(n -m) ! Explanation: Let A = {a1, a2, … am},B = {b1, b2, …, bn}, and let f : A → B. The possible choices for f (a1) are n. Having fixed f (a1), the possible choices for f (a2) are n − 1, and so on. Thus, there are n (n − 1) (n − 2) … (n − (m − 1)) = n !/(n -m) ! injective mappings from A to B. |
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