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# A set contain 4 natural no. …

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A set contain 4 natural no. And set b contain 3 alphabet find no. Of all possible onto

Manav Sharma 2 months, 1 week ago

To find the number of onto (surjective) functions from set $$A$$ to set $$B$$, where $$|A| = 4$$ and $$|B| = 3$$, we can use the formula: $\text{Number of onto functions} = |B|^{|A|} - \binom{|B|}{1} \times (|B| - 1)^{|A|} + \binom{|B|}{2} \times (|B| - 2)^{|A|} - \binom{|B|}{3} \times (|B| - 3)^{|A|}$ In this case, $$|A| = 4$$ and $$|B| = 3$$, so we have: $\text{Number of onto functions} = 3^4 - \binom{3}{1} \times 2^4 + \binom{3}{2} \times 1^4 - \binom{3}{3} \times 0^4$ $= 81 - 3 \times 16 + 3 \times 1 - 1 \times 0$ $= 81 - 48 + 3 - 0$ $= 36$ So, there are $$36$$ possible onto functions from set $$A$$ to set $$B$$.

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