SOLUTION: At bus stop, there are 11 people queueing, 7adults 4chilcdren. Calculate number of arrangements of these 11people such that FIRST and LAST people in the queue are adults?

Algebra ->  Permutations -> SOLUTION: At bus stop, there are 11 people queueing, 7adults 4chilcdren. Calculate number of arrangements of these 11people such that FIRST and LAST people in the queue are adults?      Log On


   

Question 945817: At bus stop, there are 11 people queueing, 7adults 4chilcdren. Calculate number of arrangements of these 11people such that FIRST and LAST people in the queue are adults?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
At bus stop, there are 11 people queueing, 7 adults and 4 chilcdren. Calculate
the number of arrangements of these 11 people such that FIRST and LAST people in
the queue are adults?
   (There are 7 ADULTS.)
Choose the FIRST (1st) PERSON as any of those 7 ADULTS.
   (There are now 6 ADULTS remaining.)
Choose the LAST (11th) PERSON as any of those 6 remaining ADULTS.

   (There are now 9 PEOPLE remaining.)
Choose the 2nd PERSON as any of those 9 remaining PEOPLE.
   (There are now 8 PEOPLE remaining.)
Choose the 3rd PERSON as any of those 8 remaining PEOPLE. 
   (There are now 7 PEOPLE remaining.)
Choose the 4th PERSON as any of those 7 remaining PEOPLE.
   (There are now 6 PEOPLE remaining.)
Choose the 5th PERSON as any of those 6 remaining PEOPLE.
   (There are now 5 PEOPLE remaining.)
Choose the 6th PERSON as any of those 5 remaining PEOPLE.
   (There are now 4 PEOPLE remaining.)
Choose the 7th PERSON as any of those 4 remaining PEOPLE.
   (There are now 3 PEOPLE remaining.)
Choose the 8th PERSON as any of those 3 remaining PEOPLE.
   (There are now 2 PEOPLE remaining.)
Choose the 9th PERSON as either of those 2 remaining PEOPLE.
   (There is now only 1 PERSON remaining.)
Choose the 10th PERSON as that 1 remaining PERSON.

7*6*9*8*7*6*5*4*3*2*1 = 7P2*9P9 = 15240960 ways.

Edwin