If n+5pn+1=12(11)(n−1) n+3pn then n is equal to

If $^{n + 5} p_{n + 1} = \frac{1}{2} (11) (n - 1) (^{n + 3} p_{n})$ then $n$ is equal to

A
10, 11
B
9, 10
C
8, 7
D
6,7

Solution:

$\frac{1}{2} (11) (n - 1) = \frac{^{n + 5} P_{n + 1}}{^{n + 3} P_{n}}$

$= \frac{(n + 5)!}{4!} \times \frac{3!}{(n + 3)!}$

$\Rightarrow \frac{1}{2} (11) (n - 1) = \frac{1}{4} (n + 5) (n + 4)$

$\begin{array}{ll} \Rightarrow 22 n - 22 = n^{2} + 9 n + 20 \\ \Rightarrow n^{2} - 13 n + 42 = 0 \Rightarrow n = 6, 7 \end{array}$

Related content

Distance Speed Time Formula

Refractive Index Formula

Electric Current Formula

Ohm’s Law Formula

Wavelength Formula

Electric Power Formula

Resistivity Formula

Linear Momentum Formula