Find n, If n+5Pn+1 = (n – 1). n+3Pn, find n.

Q8 of 140 Page 288

Find n, If ⁿ⁺⁵P_n+1 = (n – 1). ⁿ⁺³P_n, find n.

To find: the value of n

Formula Used:

Total number of ways in which n objects can be arranged in r places (Such that no object is replaced) is given by,

ⁿP_r

ⁿ⁺⁵P_n+1 = (n – 1). ⁿ⁺³P_n

(n - 7)(n - 6) = 0

n = 7, 6

Hence, values of n are 7 & 6

If ¹⁵P_r–1 : ¹⁶P_r–2, = 3 : 4, find r.

If ^2n–1P_n : ²ⁿ⁺¹P_n–1, = 22 : 7, find n.

Prove that 1 + 1. ¹P₁ + 2. ²P₂ + 3. ³P₃ + …. n. ⁿP_n = ⁿ⁺¹P_n+1.

Find the number of permutations of 10 objects, taken 4 at a time.