SOLUTION: Good day! Please help me in my math homework. In how many ways can 5 people be seated in a car, two in the front seat and 3 in the rear seat, if only 3 of the 5 can drive and o

Question 1063275: Good day! Please help me in my math homework.
In how many ways can 5 people be seated in a car, two in the front seat and 3 in the rear seat, if only 3 of the 5 can drive and others cannot?
Would really appreciate your help. Thank you!
Found 3 solutions by josmiceli, rothauserc, ikleyn:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
You will have 1 driver with 4 people left over
With each of the 3 possible drivers, the 4 left over
can arrange themselves
different ways. Since there can be 3 drivers,
that gives different seatings
---------------------------------------------
Note that if anyone could drive, they could be
seated different ways
---------------------------------------------
Definitely get a 2nd opinion on this.
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
The assumption is that 2 students in the front seat and 3 students in the back seat is modeled by "arranging 5 students in 5 chairs"
:
(1) Since order is not important, then we have
**************
5! = 120 ways
**************
:
(2) There are 3 possibilities for the driver's seat
3C1 = 3! / (1! * (3-1)!) = 3
so we multiply 3 times 4! = 72
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There are 72 ways if only 3 of the 5 can drive and others cannot
*************************************************************************
:

Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
There are 3 possibilities to sit at the driver's seat.

There are 4! permutations for the remaining people.

Answer. In all, there are 3*4! = 3*24 = 72 sitting arrangements.
              (If there are no other restrictions)

On Combinations and Permutations see the lessons
    - Introduction to Permutations
    - PROOF of the formula on the number of Permutations
    - Problems on Permutations
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - OVERVIEW of lessons on Permutations and Combinations
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".

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