Question

np6=30.np4 find n=?
​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

GIVEN

$\displaystyle \sf{ \: }{\large{ {}^{n} P_6}} = 30 \: . \: \large{ {}^{n} P_4}$

TO DETERMINE

The value of n

CALCULATION

$\displaystyle \sf{ \: }{\large{ {}^{n} P_6}} = 30 \: . \: \large{ {}^{n} P_4}$

$\implies \: \displaystyle \sf{ \frac{n \: ! }{(n - 6) \: ! } = 30 \: \times \: \frac{n \: ! }{(n - 4) \: ! }\: }$

$\implies \: \displaystyle \sf{ \frac{(n - 4)\: ! }{(n - 6) \: ! } = 30 \: }$

$\implies \: \displaystyle \sf{ (n - 4)(n - 5) = 30 \: }$

$\implies \: \displaystyle \sf{ {n}^{2} - 9n - 10 =0 }$

$\implies \: \displaystyle \sf{ {n}^{2} - 10n + n- 10 =0 }$

$\implies \: \displaystyle \sf{ (n - 10) ( n + 1) =0 }$

$\implies \: \displaystyle \sf{n = - 1 \: \: , \: 10 }$

Since n is a positive integer

So

$\sf {n \ne\: - 1 }$

$\therefore \: \sf{ n = 10}$

━━━━━━━━━━━━━━━━

LEARN MORE FROM BRAINLY

How many byes will be given if 32 teams are participating in a knock-out tournament

https://brainly.in/question/24215389