Solution - Episode 2; The Warthog and Mongeese

The question:

There are seven students going on a journey together and they need to get seating arrangements completed To ride in they have one warthog ( which can seat 3 people) and two Mongeese (which can hold 2 people each). If Richard, Lawrence and Justus all have to sit together, and Roxanne can sit with anyone, how many ways can everyone be seated?

Remember, where each person sits DOES matter, and the mongeese themselves are distinguishable.

The Solution.




The answers are above this very text and if you double click it it will enlarge i think. but if it does not work i will guide you on how to do it. (HINT: I would recommend to click the image cause there are some diagrams)
Step 1.) Find the number of ways to seat Lawrence, Richard , and Justus
- All must sit together so therefore they must be in a warthog
- Since order does matter, the number of ways to seat them is "3!" which is equal to 6

Step 2.) Find the number of ways to seat Roxanne and the other students.
-The two seat ones (s1), and the two seat two's (s2) are non-distinguishable objects therefore the number of ways to seat the students in the mongeese is 4 factorial (4!) all over 2 factorial (2!) times 2 factorial (2!) which will give you 6

Now for step 3

Step 3.) Total number of ways to seat everyone is (# of ways to seat Lawrence, Richard, and Justus) ( # of ways to seat Roxanne and the rest of the students.

(6)(6) = Which the total ways to seat everyone is 36. Ta-Da!