SOLUTION: Seven cheerleaders line up to enter a gym at the start of a basketball game. Three carry signs and four carry pom-poms. How many different ways can they form their line if the fir

Algebra ->  Permutations -> SOLUTION: Seven cheerleaders line up to enter a gym at the start of a basketball game. Three carry signs and four carry pom-poms. How many different ways can they form their line if the fir      Log On


   

Question 1115533: Seven cheerleaders line up to enter a gym at the start of a basketball game. Three carry signs and four carry pom-poms. How many different ways can they form their line if the first in line and the last must be sign carriers?
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  Of the three sign carrier, you have 6 options to assign one of them to be the first and the second to be the last.

        Then the third sign carrier will be defined by an unique way.



2.  You have 4! = 24 permutations to arrange 4 pom-poms carriers.



3.  Finally, you can place the remained third sign carrier on any of 5 positions before or between or after four pom-poms carriers.



4.  In all, you have  6*24*5 = 720  different arrangements.

Solved.