Question

If 3.^{(n + 3)}p₄ = 5.^{(n + 2)}p₄ then find the value of n.

Answer 1

3.^{(n + 3)}p₄ = 5.^{(n + 2)}p₄

∴ 3.(n + 3) (n + 3 – 1) (n + 3 – 2) (n + 3 – 3) [According to definition of nPr]

= 5.(n + 2) (n + 2 – 1) (n + 2 – 2) (n + 2 – 3) 3.(n + 3) (n + 2) (n + 1) (n)

= 5.(n + 2) (n + 1) (n) (n- 1)

∴ 3(n + 3) = 5(n – 1)

∴ 3n + 9 = 5n – 5

∴ 9 + 5 = 5n – 3n

∴ 14 = 2n

∴ n = 142 = 7