Question

The number of permutation of 4 letters at a time from the word 'PARABOLA' is

• A. 360
• B. 500
• C. 60
• D. 10

Answer 1

Answer: (B)

500

Answer 2

Total letters = 8 (1P, 3A, 1R, 1B, 1O, 1L)

Case I: 3 letters alike, 1 different $1x^{5}C_{1}\frac{4!}{3!} = 20$.

Case II: 2 letters alike, 2 different $1x^{5}C_{2}\frac{4!}{3!} = 120$

Case III: All letters different $6C_{4}4! = 360$

Total = 500.