Question

if nc3:(n-1)c4=8:5 then n=​

Answer 1

Answer:

The value of n is 8

Step-by-step explanation:

$\text{Given: }$

$n_{C_3}:(n-1)_{C_4}=8:5$​

$\implies\frac{n_{C_3}}{(n-1)_{C_4}}=\frac{8}{5}$​

$\implies\:5(n_{C_3})=8\,(n-1)_{C_4}$​

$\boxed{\bf\:n_{C_r}=\frac{n!}{(n-r)!\,r!}}$

$\implies\:5(\frac{n!}{(n-3)!\,3!})=8(\frac{(n-1)!}{(n-5)!\,4!})$​

Using

$\boxed{n!=(n-1)!\,n}$

$\implies\:5(\frac{(n-1)!\,n}{(n-5)!(n-4)(n-3)\,3!})=8(\frac{(n-1)!}{(n-5)!\,3!\,4})$​

$\implies\:5(\frac{n}{(n-4)(n-3)})=8(\frac{1}{4})$​

$\implies\:5n=2(n-4)(n-3)$​

$\implies\:5n=2(n^2-7n+12)$​

$\implies\:2n^2-19n+24=0$​

$\implies\:2n^2-16n-3n+24=0$​

$\implies\:2n(n-8)-3(n-8)=0$​

$\implies\:(2n-3)(n-8)=0$​

$\implies\:n=8,3/2$​

$\text{since n is an integer, n=8}$

Answer 2

Answer:

Step-by-step explanation:Answer:

The value of n is 8

Step-by-step explanation:

\text{Given: }

n_{C_3}:(n-1)_{C_4}=8:5​

\implies\frac{n_{C_3}}{(n-1)_{C_4}}=\frac{8}{5}​

\implies\:5(n_{C_3})=8\,(n-1)_{C_4}​

\boxed{\bf\:n_{C_r}=\frac{n!}{(n-r)!\,r!}}

\implies\:5(\frac{n!}{(n-3)!\,3!})=8(\frac{(n-1)!}{(n-5)!\,4!})​

Using

\boxed{n!=(n-1)!\,n}

\implies\:5(\frac{(n-1)!\,n}{(n-5)!(n-4)(n-3)\,3!})=8(\frac{(n-1)!}{(n-5)!\,3!\,4})​

\implies\:5(\frac{n}{(n-4)(n-3)})=8(\frac{1}{4})​

\implies\:5n=2(n-4)(n-3)​

\implies\:5n=2(n^2-7n+12)​

\implies\:2n^2-19n+24=0​

\implies\:2n^2-16n-3n+24=0​

\implies\:2n(n-8)-3(n-8)=0​

\implies\:(2n-3)(n-8)=0​

\implies\:n=8,3/2​

\text{since n is an integer, n=8}