Question

If nP4 = 30 * nP2 , then the value of n is

Answer 1

"n = 8"

ⁿP4 = n!/(n-4)!
= {n(n-1)(n-2)(n-3)(n-4)!]/(n-4)!
= n(n-1)(n-2)(n-3)

ⁿP2 = n!/(n-2)!
= {n(n-1)(n-2)!]/(n-2)!
= n(n-1)

Now, according to Question:

ⁿP4 = 30 * ⁿP2
→ [n(n-1)(n-2)(n-3)] = 30 * [n(n-1)]
→ (n-2)(n-3) = 30
→ n² -5n + 6 - 30 = 0
→ n² - 5n - 24 = 0
→ n² - 8n + 3n - 24 = 0
→ n(n - 8) + 3(n - 8) = 0
→ (n - 8)(n + 3) = 0
→ n = 8, -3

Now, "n" cannot be negative, So, n = 8

Thankyou!!!