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

Question

Question

This question was previously asked in

NDA-I (Mathematics) Official Paper (Held On: 21 Apr, 2024)

Answer 1

Concept:

Number of onto function from a set A (containing m elements) to a set B (containing n elements) (m ≥ n) is given by

n^m - ⁿC₁(n - 1)^m + nC2(n - 2)m - ...

Explanation:

A = {1, 2, 3, 4, 5}, B = {6, 7}

n(A) = m = 5 and n(B) = n = 2

So number of onto functions from A to B is

2⁵ - 2C1(2 - 1)5

= 32 - 2 = 30

Option (3) is true.

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