Mock test

Question

The number of ways possible to form injective function from set A to set B, where set ‘A’ has 3 elements, set ‘B’ has 5 elements such that i^th element of set A should not be matched with i^th element of set B

Comments

Is it 24?

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ans 32

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https://gateoverflow.in/170311/discrete-maths-functions

Total injective functions = 5$\times$ 4$\times$3 = 60

when ALL ith element map to ith element = 1 function

when Two ith element map to ith element = chose any 2 element from a ³c₂ then for 1 element we have 3 choice = 3$\times$3 = 9

when 1 element map to ith element = ³c₁ $\times$ 4$\times$3= 36

Required = 60 - [ 36-9+1] = 32

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@ Anu Thanks for the link. It helped me rectify the mistake I was making.

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:)..

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when 1 element map to ith element = 3c1 × 4×3= 36

please explain me 3???

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Out of the 3 elements we have chosen 1 element which will be mapped to its corresponding ith element in 3C1 ways and the other two can now be linked in 4 * 3 ways. @ Anu007 Hope my explanation is correct.

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other two can be lnked in 2*4  ways ??

bcs a has 2 remaining element

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A has 2 remaining elements and B has 4 remaining elements. So one of the elements of A can be linked to one of the 4 elements of B and the other element to the remaining 3. Therefore, 4*3.

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Apply principle of inclusion-exclusion  ans = 32