Question:
Let $x$ denote the total number of one-one functions from a set $A$ with 3 elements to a set $B$ with 5 elements and $y$ denote the total number of one-one functions from the set $A$ to the set $A \times B$. Then:
Correct Option: , 2
Solution:
Number of elements in $A=3$
Number of elements in $\mathrm{B}=5$ Number of elements in $A \times B=15$
Number of one-one function $x=5 \times 4 \times 3$
$x=60$
Number of one-one function $y=15 \times 14 \times 13$
$y=15 \times 4 \times \frac{14}{4} \times 13$
$y=60 \times \frac{7}{2} \times 13$
$2 y=(13)(7 x)$
$2 y=91 x$
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