A) \[^{n}{{P}_{2}}\]
B) \[{{2}^{n}}-2\]
C) \[{{2}^{n}}-1\]
D) None of these
Correct Answer: B
Solution :
[b] we know that, if X and Y are any two finite sets having m and n elements respectively, where \[1\le n\le m,\] then the number of onto functions from X to Y is given by \[\sum\limits_{r=1}^{n}{{{(-1)}^{n-r}}^{n}{{C}_{r}}{{r}^{m}}\cdot \,\,r=1}\] Thus, the number of subjective mappings is \[\sum\limits_{r=1}^{2}{{{(-1)}^{2-r}}{{C}_{r}}{{r}^{n}}=\left( {{2}^{n}}-2 \right)}\]
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