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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

Posted by Dharun S 1 month, 2 weeks ago

CBSE > Class 12 > Mathematics

1 answers

Manav Sharma 1 month, 2 weeks 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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