If-n-P-r-n-C-r-1-5-find-the-value-of-r-

Question Number 49982 by pieroo last updated on 12/Dec/18

If \frac{n_{P_{r}}}{n_{C_{r}}} - 1 = 5, find the value of r

Answered by ajfour last updated on 13/Dec/18

^{n} P_{r} = \frac{n!}{(n - r)!} &^{n} C_{r} = \frac{n!}{r! (n - r)!}

\Rightarrow \frac{^{n} P_{r}}{^{n} C_{r}} - 1 = r! - 1 = 5

\Rightarrow r! = 6 \Rightarrow r = 3 .

Commented by ajfour last updated on 13/Dec/18

2! = 2, 4! = 24

\Rightarrow 2! < r! < 4!

l e t s c h e c k 3! = 1 \times 2 \times 3 = 6

\Rightarrow r! = 6 \Rightarrow r = 3 .

Commented by pieroo last updated on 13/Dec/18

thanks sir, But how do i explain to

my younger brother that r! = 6 \Rightarrow r = 3 ?

Commented by pieroo last updated on 13/Dec/18

wow, thank you very much for your patience .

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