Question 115

If A and B are two sets such that n(A) = 4 and n(B) = 5, then the number of non-constant functions from A into B is

Solution

If X has m elements and Y has n elements, the number if onto functions are,

$$n^m-\left(\begin{array}{c}n\\ 1\end{array}\right)(n-1)^{m} + \left(\begin{array}{c}n\\ 2\end{array}\right)(n-2^{m}) + ................+(-1)^{n-1}\left(\begin{array}{c}n\\ n-1\end{array}\right)1^{m}$$

here m= 5 and n= 4 put the value and we get

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TS ICET 23rd May 2019 Shift-1

If A and B are two sets such that n(A) = 4 and n(B) = 5, then the number of non-constant functions from A into B is

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