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

Posted by Dharun S 1 year, 1 month ago

CBSE > Class 12 > Mathematics

1 answers

Manav Sharma 1 year, 1 month 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

$B$ .

0Thank You

ANSWER

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