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Let A= a, b, c, d, e, f and B= 1,2,3 are two sets. Let m denotes the number of mappings which are into from A to B n denotes the number of mappings which are injective from B to A . Find (m+n) .

Correct answer

309

Step-by-step solution

m = into mappings from A to B Case-I: If exactly one element of set B is not the image of any of the elements of set A then total number of into functions are ^3 C₁ (2^6-2 )=3 62=186 Case-II: If exactly two elements of set B is not the image of any of the elements of set A then total number of into functions are ^3 C₂ 1=3 and hence m=186+3=189

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