Question

Find the number of ways to arrange 6 distinct books on a shelf if 2 specific books must be adjacent.

• A. 120
• B. 240
• C. 360
• D. 480

Hint:

Treat adjacent items as a single unit, arrange units, and multiply by internal arrangements of the unit.

Answer 1

The Correct Option is B

- Step 1: Group the 2 books. Treat the 2 specific books as one unit. Units: 1 (pair) + 4 others = 5 units.
- Step 2: Arrange units. $5! = 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 = 120$.
- Step 3: Arrange within pair. The 2 books can be arranged in $2! = 2$ ways.
- Step 4: Total arrangements. $120 \times 2 = 240$.
- Step 5: Alternative. Total arrangements: $6! = 720$. Adjacent pairs (e.g., 1-2, 2-3, etc.): 5 ways. Pair arrangements: $2! = 2$. Other 4 books: $4! = 24$. Total = $5 \times 2 \times 24 = 240$.
- Step 6: Verify. Both methods give 240, matching option (2).
- Step 7: Conclusion. Option (2) 240 is correct.