If $^{n} P_{7} = 42 \cdot^{n} P_{5}$ , then find $n$

Open in App

Solution

Fact: $^{n} P_{r} = \frac{n!}{(n - r)!}$

Given $^{n} P_{7} = 42 \cdot^{n} P_{5}$

$\Rightarrow \frac{n!}{(n - 7)!} = 42 \cdot \frac{n!}{(n - 5)!}$
$\Rightarrow (n - 5) (n - 6) = 42 = 7 \times 6$
$\Rightarrow n - 5 = 7$
$∴ n = 12$

Suggest Corrections

Similar questions

^{n} P_{7} = 42. (^{n} P_{5})

n

^{n} P_{7} = 42 \times^{n} P_{5}

n =

^{n} P_{5} = 42

^{n} P_{3}

n > 4

^{n} P_{5} : n - 1 P_{5} = 3 : 2

n

n

(i)^{n} P_{5} = 42^{n} P_{3}, n > 4

(i i) \frac{^{n} P_{4}}{^{n - 1} P_{4}} = \frac{5}{3}, n > 4

Join BYJU'S Learning Program