Let A=\1,2,3,4,5\ and B=\6,7\ . What is the number of onto functions from A to B ?

Correct answer: (C) 30. n(~A)=5 and n(~B)=2 Number of onto functions =2^5-^2 C_1(2-1)^5 =32-2=30 .

Q185 / 270 · NDA 2024 (Phase 1) · Mathematics

Let $\mathrm{A}=\{1,2,3,4,5\}$ and $\mathrm{B}=\{6,7\}$. What is the number of onto functions from A to B ?

A
10
B
20
Correct answer
C
30
D
32

Solution

$n(\mathrm{~A})=5$ and $n(\mathrm{~B})=2$ $\begin{gathered}\text { Number of onto functions }=2^5-{ }^2 \mathrm{C}_1(2-1)^5 \\ =32-2=30 .\end{gathered}$

Hence, the correct answer is option: 'C'.

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