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(B) The number of one-one functions from a set with $n$ elements to a set with $m$ elements $(m \ge n)$ is given by $P(m, n) = \frac{m!}{(m-n)!}$.For

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$2y=91x$

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(B) The number of one-one functions from a set with $n$ elements to a set with $m$ elements $(m \ge n)$ is given by $P(m, n) = \frac{m!}{(m-n)!}$.For $x$,the set $A$ has $3$ elements and set $B$ has $5$ elements. Thus,$x = P(5, 3) = 5 	imes 4 	imes 3 = 60$.For $y$,the set $A$ has $3$ elements and the set $A 	imes B$ has $3 	imes 5 = 15$ elements. Thus,$y = P(15, 3) = 15 	imes 14 	imes 13 = 2730$.Now,we compare $x$ and $y$:$x = 60$$y = 2730$Calculating the ratio $\frac{y}{x} = \frac{2730}{60} = \frac{273}{6} = \frac{91}{2}$.Therefore,$2y = 91x$.

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 ...... .

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