Let A = {(x, y) : 2x + 3y = 23, x, y ∈ N} and B = {x : (x, y) ∈ A}. Then the number of one-one functions

Question

Let \(A=\{(x, y): 2 x+3 y=23, x, y \in N\}\) and \( B=\{x:(x, y) \in A\}\). Then the number of one-one functions from A to B is equal to ______.

Answer 1

Correct answer is :  24 

\(2 \mathrm{x}+3 \mathrm{y}=23, \quad \mathrm{x}, \mathrm{y} \in \mathrm{N}\) 

\(\mathrm{A}=\{(1,7),(4,5),(7,3),(10,1)\}\) 

\(\mathrm{B}=\{1,4,7,10\}\) 

\(\text { then no. of one-one }\)\(f^n = 4! = 24\)