If a set A has m elements and set B has n ele | vedclass

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(D) Given,$|A| = m$ and $|B| = n$. The total number of injective functions from $A$ to $B$ is given by the formula $^nP_m = \frac{n!}{(n-m)!} = 2520$.

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(D) Given,$|A| = m$ and $|B| = n$. The total number of injective functions from $A$ to $B$ is given by the formula $^nP_m = \frac{n!}{(n-m)!} = 2520$. We need to express $2520$ as a product of consecutive integers starting from $n$ down to $(n-m+1)$. $2520 = 7 	imes 6 	imes 5 	imes 4 	imes 3$. This is equivalent to $^7P_5 = \frac{7!}{(7-5)!} = \frac{7!}{2!} = 7 	imes 6 	imes 5 	imes 4 	imes 3 = 2520$. Comparing $^nP_m$ with $^7P_5$,we get $n = 7$ and $m = 5$. Thus,$m = 5$.

If a set $A$ has $m$ elements and set $B$ has $n$ elements and the number of injections from $A$ to $B$ is $2520$. Then,$m$ is equal to

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