Question

how many function are there between two sets having no. of element​

Answer 1

Answer:

Number of functions from one set to another: Let X and Y are two sets having m and n elements respectively. In a function from X to Y, every element of X must be mapped to an element of Y. Therefore, each element of X has 'n' elements to be chosen from. Therefore, total number of functions will be n×n×n

Answer 2

Answer:

$If m>nm>n, there aren't any.</p><p></p><p>If m≤nm≤n, there are nn options for where to send the first element, n−1n−1 options for the second, n−2n−2 for the third and so on.</p><p></p><p>So, the total number of 1:1 functions from an mm-set to an nn-set is</p><p></p><p>n(n−1)(n−2)⋯(n−m+1)=n!(n−m)!</p><p></p><p>$

Step-by-step explanation:

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