EasyMathematicsHigh School (11–12)Algebra › Permutations and CombinationsNumericalBoard ExamA-LevelIB
Seven friends take seven seats in a row at the cinema…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Seven friends take seven seats in a row at the cinema. Neha and Omar want to sit side by side.
- In how many ways can the friends sit with Neha and Omar together?
- In how many ways can they sit with Neha and Omar apart?
Need a reminder? The key ideaShow
Together: glue the objects into one block, and multiply by the orders inside it. Never together: all arrangements minus the together ones. Fill restricted places first; a number cannot start with . The rank of a word is the number of words before it in dictionary order, plus .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Glue. The block and the other friends make units: orders.
Step 2. Inside the block. Neha and Omar have orders. Together: .
Step 3. Apart. All seatings: . Apart: .
Answer: together and apart.
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