MediumMathematicsHigh School (11–12)Algebra › Permutations and CombinationsNumericalBoard ExamA-LevelIB
In how many ways can the letters of the word ORANGE be arranged so that the vowels stand only in…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
In how many ways can the letters of the word ORANGE be arranged so that the vowels stand only in the odd places?
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. The places. The odd places are , and .
Step 2. The vowels. O, A and E fill them in ways.
Step 3. The consonants. R, N and G fill places , and in ways.
Answer: arrangements.
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