LetnA=4 and nB=5. The number of all possible many-one functions from A to B is

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Let $n (A) = 4$ and $n (B) = 5$ . The number of all possible many-one functions from A to B is

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120

505

625

answer is D.

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Detailed Solution

Given that $n (A) = 4$ and $n (B) = 5$

The number of many to one functions is $t o t a l n u m b e r o f f u n c i t o n s - t o t a l n u m b e r o f o n e o n e f u n c i t o n s$

Hence, $5^{4} - 5_{P_{4}} = 625 - 120 = 505$

Therefore, the number of many to one functions from the set A to the set B is $505$

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