Let A = {1, 3, 7, 9, 11} and B = {2, 4, 5, 7, 8, 10, 12}. Then the total number of one-one maps

Question

Let \(\mathrm{A}=\{1,3,7,9,11\}\) and \(\mathrm{B}=\{2,4,5,7,8,10,12\}\).

Then the total number of one-one maps \(\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}\), such that \(\mathrm{f}(1)+\mathrm{f}(3)=14\), is :

(1) 180

(2) 120

(3) 480

(4) 240

Answer 1

Correct option is (4) 240

\(\mathrm{A}=\{1,3,7,9,11\}\)

\(\mathrm{B}=\{2,4,5,7,8,10,12\}\)

\(\mathrm{f}(1)+\mathrm{f}(3)=14\)

(i) \(2+12\)

(ii) \(4+10\)

\(2 \times(2 \times 5 \times 4 \times 3)=240\)