This problem is concerned with a simple visual messaging system based on an orde

Question

This problem is concerned with a simple visual messaging system based on an ordered arrangement of ten colored flags. A message is formed by placing ten colored flags on a single flagpole. The message is read by noting the colors of the flags starting at the top of the pole and moving down. Suppose that the ten flags consist of two red flags, three blue flags, and five green flags. a) How many different messages can be formed from these ten flags? b) How many different messages can be formed from those ten flags if the first and last flags must be red? c) How many different messages can be formed from those ten flags if the fifth and sixth flags must be red? d) How many different messages can be formed from these ten flags if the every other flag, starting with the first must be green?

Explanation / Answer

a) total number of ways =10!/(2!*3!*5!) =2520

b)if first and last is red that means we need to arrange remaining 8 ; number of ways =8!/(5!*3!) =56

c)as this si similar to previous problem ; number of ways =56

d) here all green are placed in odd number of places hence number of ways to distribute remaining 5 flags =5!/(3!*2!) =10

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.