Let A=1,3,7,9,11 and B=2,4,5,7,8,10,12.

Question

Let $A={1,3,7,9,11}$ and $B={2,4,5,7,8,10,12}$. Then the total number of one-one maps $f:A	o B$, such that $f(1)+f(3)=14$, is :

Accepted Answer

$f(1)+f(3)=14$

Case I

$$\begin{aligned}
& f(1)=2, f(3)=12 \
& f(1)=12, f(3)=2
\end{aligned}$$

Total one-one function

$$\begin{aligned}
& =2 \times 5 \times 4 \times 3 \
& =120
\end{aligned}$$

Case II

$$\begin{aligned}
& f(1)=4, f(3)=10 \
& f(1)=10, f(3)=4
\end{aligned}$$

Total one-one function

$$\begin{aligned}
& =2 \times 5 \times 4 \times 3 \
& =120 \
& \text { Total cases }=120+120=240
\end{aligned}$$

Solutions · 1