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Let \mathrm{R=\{a, b, c, d\}} and \mathrm{S=\{1,2,3\}}, then the number of functions \mathrm{f}, from \mathrm{R} to \mathrm{S}, which are onto is

Option: 1

81


Option: 2

16


Option: 3

24


Option: 4

36


Answers (1)

best_answer

Total number of functions = 3^{4}.

All the four elements can be mapped to exactly one element in 3 ways, and exactly two elements in 3\left(2^{4}-2\right).

Thus, the number of onto functions =3^{4}-3-$ $3\left(2^{4}-2\right)=36.

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avinash.dongre

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