Question

The no. of different ways, the letters of the word KUMARI can be placed in the 8 boxes of the given figure so that no row remains empty will be ______.

विकल्प

• 18720

• 18721

• 18722

• 18723

Answer 1

The no. of different ways, the letters of the word KUMARI can be placed in the 8 boxes of the given figure so that no row remains empty will be 18720.

Explanation:

KUMARI have 6 different letter

No. of their arrangements in boxes so that each contains at least one letter

= Coefficient of x⁶ in 6! (⁴C₁x + ⁴C₂x² + ⁴C₃x³ + ⁴C₄x⁴) × (²C₁x + ²C₂x²)²

= Coefficient of x⁶ in 6! (4x + 6x² + 4x³ + x⁴) × (2x + x²)²

= Coefficient of x⁶ in 6! (4x + 6x² + 4x³ + x⁴) × (4x² + x⁴ + 4x³)

= 6! × (6 + 16 + 4)

= 6! × 26

= 720 × 26 

= 18720