Let A = {1, 2, 3, ldots, n} and B = {a, b}. I | vedclass

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(C) The number of onto functions from a set $A$ with $n$ elements to a set $B$ with $m$ elements is given by $m^n - \binom{m}{1}(m-1)^n + \binom{m}{2}

Vedclass · Accepted Answer

$20$

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(C) The number of onto functions from a set $A$ with $n$ elements to a set $B$ with $m$ elements is given by $m^n - \binom{m}{1}(m-1)^n + \binom{m}{2}(m-2)^n - \ldots$.Here,$m = 2$ and $n = n$. The number of onto functions is $2^n - \binom{2}{1}(2-1)^n = 2^n - 2$.Given $2^n - 2 = 62$,we have $2^n = 64$,which implies $n = 6$.The number of subsets of $A$ containing exactly three elements is given by $\binom{n}{3} = \binom{6}{3}$.Calculating this,$\binom{6}{3} = \frac{6 	imes 5 	imes 4}{3 	imes 2 	imes 1} = 20$.

Let $A = \{1, 2, 3, \ldots, n\}$ and $B = \{a, b\}$. If the number of onto functions from $A$ to $B$ is $62$,then the number of subsets of $A$ containing exactly three elements is:

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