GATE | GATE MOCK 2017 | Question 36

A and B are two sets. If |A| = 5 , |B| = 3 , then, the number of onto functions from A to B are ___ ?

(A) 35
(B) 150
(C) 29
(D) 27


Answer: (B)

Explanation:

Given, m=5 , n=3
Number of onto function = ??−??1(?−1)?+??2(?−2)?−??3(?−3)?+??4(?−4)?

= 35 – 3c1(2)5 + 3c2 (1)5 – 3c3 (0)5
= 243 – 3×32 + 3×1

= 150


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