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Permutations , combinations and binomial expansion — Statistics STD 11 Commerce — Question

Gujarat BoardEnglish MediumSTD 11 CommerceStatisticsPermutations , combinations and binomial expansion1 Mark
Question
If $n P _{ 3 }=210$, find the value of $n$.
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Answer

$n P_3=210$
$\therefore \frac{n!}{(n-3)!}=210$
$\therefore \frac{n(n-1)(n-2)=210}{(n-3)!}=210$
$\therefore n(n-1)(n-2)=210$
$\therefore n(n-1)(n-2)=7 \times 6 \times 5=7(7-1)(7-2)$
$\therefore n =7$, Hence, $n =7$

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