DM - Functions & Relations -Q12

+1 vote

Number of onto functions from a set of n elements (n>2) to set of 3 elements?

(A). 3^n-3

(B). 3^n-3.2^n-3

(C). 3^n-3.2^n+3

(D). 3^n-2^n-13

asked Jun 24 in Discrete Maths by gbeditor (44,490 points)
reshown 6 days ago by gbeditor

1 Answer

+1 vote
 
Best answer
This can be done using inclusion and exclusion principles.

Total functions: 3^n

Now, we find the number of functions which are not onto.

Case 1: One element of RHS is not mapped. Every element in LHS will have two choices, hence 2^n, 3 times.

Case 2: Two elements of RHS are not mapped. Every element in LHS will have only one choice. Hence, 1.3

Case 3: Three elements of RHS are not mapped. Zero functions possible.

Hence, answer will be 3^n - 3.2^n + 3
answered 4 days ago by deepak-gatebook (112,390 points)
Answer:
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