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Number of onto functions from \(A\) to \(B\) if \(n(A)=6\) and \(n(B)=3\) is |
\(2^6-2\) \(3^6-3\) \(340\) \(540\) |
\(540\) |
No. of surjective functions if $n(A)=m$ and $n(B)=n$ $⇒\sum\limits_{r=1}^n(-1)^{n-r}×{^nC}_r×r^m$ $=\sum\limits_1^3(-1)^{3-r}{^3C}_r×r^6$ $=({^3C}_1×1^6)-({^3C}_2×2^6)+({^3C}_3×3^6)$ $=540$ |
