Question

Find the number of ways in which 10 different flowers can be strung to form a garland so that three particular flowers are always together

(a) \(\frac{9!\times3!}{2}\) 

(b) \(\frac{7!\times3!}{2}\)

(c) \(\frac{8!\times3!}{2}\)

(d) 7 ! × 2 !

Answer 1

(b)  \(\frac12\) (7! × 3!)

Consider the three particular flowers as one flower. Then we have (10 – 3) + 1 = 8 flowers which can be strung in the garland. 

Thus the garland can be formed in (8 – 1)!, i.e., 7! ways But the 3 particular flowers can be arranged amongst themselves in 3! ways. 

∴ Required number of ways = \(\frac12\) (7! × 3!)