To Prove: ⁹P₃ + 3 × ⁹P₂ = ¹⁰P₃

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

The equation given below needs to be proved i.e

⁹P₃ + 3 × ⁹P₂ = ¹⁰P₃.

+

(9 × 8 × 7) + (3 × 9 × 8) = 10 × 9 × 8

10 × 9 × 8 = 10 × 9 × 8

Hence, proved.

⁹P₃ + 3 × ⁹P₂ = ¹⁰P₃.