Question

The number of ways in which 12 different flowers can be strung to form a garland, so that 5 particular flowers are never separated, is equal to

• A. 302400
• B. 259200
• C. 86400
• D. 7200

Answer 1

Answer: (A)

302400

Answer 2

Treat the 5 particular flowers as a single unit. This reduces the number of items to arrange to (12 - 5) + 1 = 8 distinct units. The number of ways to arrange these 8 units in a circle, considering reflections as identical (for a garland), is $\frac{(8-1)!}{2} = \frac{7!}{2}$. The 5 particular flowers within their unit can be arranged in $5!$ ways. Thus, the total number of ways is $\frac{7!}{2} \times 5! = \frac{5040}{2} \times 120 = 2520 \times 120 = 302400$.