Number of 7-Letter Words Starting with B from BIOLOGY | Permutations Answer 360

Problem Breakdown

The word BIOLOGY contains letters: B(1), I(1), O(2), L(1), G(1), Y(1). We need to form 7-letter words starting with B using these letters exactly once each (with repetition limits respected).

• Step 1: Fix first letter as B (uses the only B available)
• Step 2: Arrange remaining 6 letters: I, O, O, L, G, Y
• Step 3: Since O is repeated twice, use multiset permutation formula

Step-by-Step Solution

1. Letters: B(1), I(1), L(1), G(1), Y(1), O(2)
2. Fix first letter: B (position 1 uses the only B)
3. Remaining letters: I, O, O, L, G, Y (6 letters, O repeated 2x)
4. Permutations for positions 2-7: 6! / 2! = 720 / 2 = 360

Exam Tips

• Multiset formula: n! / (n₁! × n₂! × ...) where nᵢ are repetition counts
• Fixed position: Fix required letter first, then arrange remaining multiset
• Practice words: “MISSISSIPPI”, “COMMITTEE”, “BOOKKEEPER”