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Permutations — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPermutations2 Marks
Question
Evaluate the following: $^{10}\text{P}_3$
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Answer

We have, $^{10}\text{P}_4 = \frac{10!}{(10-4)!}\Big[\because\ ^\text{n}\text{P}_\text{r}=\frac{\text{n!}}{(\text{n}-\text{r})!}\Big]$$=\frac{10!}{6!}$
$= \frac{10\times9\times8\times7 \times6!}{6!}$ $= 5040$ Hence, $^{10}\text{P}_4= 5040$

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