Consider the following statements a. The number of ways to arrange the letters of the word ''PEPPER'' is 60.

Question

Consider the following statements:

a. The number of ways to arrange the letters of the word ''PEPPER'' is 60.

b. In a group of 20 people, the number of ways to select a committee of 3 members where the order doesn''t matter is C(20,3).

c. The expansion of (2 + x)^3 using binomial theorem is 8 + 6x + 12x² + x³.

d. The number of ways 3 boys and 3 girls sit in a row is 360.

Which of the following statement is correct?

1. A. c and d
2. B. b and c
3. C. a and b (Correct answer)
4. D. d and a

Correct Answer

Option C — a and b

Detailed Solution & Explanation

The correct answer is a and b.

Key Points

• a: PEPPER arrangements = 6!/(3!×2!×1!) = 720/12 = 60 ✓. b: C(20,3) for committee of 3 from 20 ✓. c: (2+x)³ = 8+12x+6x²+x³ (not 6x+12x²) ✗. d: 6 people in a row = 6!=720, not 360 ✗.
• Statements a and b are correct.

Additional Information

• Arrangements of a word with repeated letters use n! ÷ (p! q! …), dividing by the factorial of each repetition count.
• PEPPER has 6 letters with P three times and E twice, giving 6!/(3!·2!) = 60.
• Use permutations (ⁿPᵣ) when order matters and combinations (ⁿCᵣ) when it does not — a committee is a combination, a seating arrangement a permutation.
• The binomial expansion of (a + b)³ is a³ + 3a²b + 3ab² + b³, so (2 + x)³ = 8 + 12x + 6x² + x³.