Question
Find the unknown value: ${ }^{n} C_{n-2}=15$
✓
Answer
$\therefore \frac{n !}{(n-2) !(n-n+2) !}=15$
$ \therefore \frac{n(n-1)(n-2) !}{(n-2) ! 2 !}=15$
$ \therefore \frac{n(n-1)}{2}=15$
$ \therefore n(n-1)=30$
$ \therefore n(n-1)=6 \times 5$
$ \therefore n(n-1)=6(6-1)$
$ \therefore n=6$
$ \therefore \frac{n(n-1)(n-2) !}{(n-2) ! 2 !}=15$
$ \therefore \frac{n(n-1)}{2}=15$
$ \therefore n(n-1)=30$
$ \therefore n(n-1)=6 \times 5$
$ \therefore n(n-1)=6(6-1)$
$ \therefore n=6$
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