AP EAMCET · Maths · Functions
If a set \(\mathrm{A}\) has \(\mathrm{n}\) elements, then the number of functions defined from A to A that are not one-one is
- A \((n)^{n^2}\)
- B \(\mathrm{n} !-\left({ }^{\mathrm{n}} \mathrm{C}_0+{ }^{\mathrm{n}} \mathrm{C}_1+{ }^{\mathrm{n}} \mathrm{C}_2+\ldots+{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{n}}\right)\)
- C \(\mathrm{n}^{\mathrm{n}}-\mathrm{n} !\)
- D \(\mathrm{n}^{\mathrm{n}}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{n}^{\mathrm{n}}-\mathrm{n} !\)
Step-by-step Solution
Detailed explanation
No. of functions from \(A\) to \(A=n^n\) No. of one-one functions \(=\frac{n !}{(n-n) !}=n !\) \(\therefore \quad\) No. of functions defined from \(A\) to \(A\) that are not oneone \(=n^n-n !\)
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