MediumMathematicsHigh School (11–12)Algebra › Permutations and CombinationsNumericalBoard ExamA-LevelIB
How many 4-letter words, with or without meaning, can be made from the letters of EDUCATION, if…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
How many -letter words, with or without meaning, can be made from the letters of EDUCATION, if each word has vowels and consonants and no letter is used twice?
Need a reminder? The key ideaShow
If someone must be in, choose the rest from the others; if someone must be out, choose from the others. Choices from separate groups multiply. For "at least one", subtract the selections with none from the total. To make words or codes, select first, then arrange the chosen things in ways.
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 letters. Vowels: E, U, A, I, O. Consonants: D, C, T, N.
Step 2. Select. choices of letters.
Step 3. Arrange. Each choice of letters gives words.
Answer: words.
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