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Let A and B be two finite sets having m and n elements respectively. Then the total number of mappings from A to B isA. `n^(m)`B. `""^(n)C_(m)`C. `""^(n)C_(m)xxm!`D. `m^(n)` |
Answer» In order to define a one-one function from A to B, we associate different elements of set A to distinct elements in set B. This is possible only when `ngem`. To determine the total number of one-one functions from A to B we first seletct m elements from B and then elements in A are associated to elements in B. The first part con be done in `""^(n)C_(m)` ways and the second part in m! ways. Hence, total number of one-one functions `=""^(n)C_(m)xxm!` |
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