HardMathematicsHigh School (11–12)Algebra › Permutations and CombinationsNumericalBoard ExamA-LevelIB
The word ALLAHABAD has 9 letters. How many arrangements of its letters are there? …
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
The word ALLAHABAD has letters.
- How many arrangements of its letters are there?
- In how many of them do all four A's stand together?
Need a reminder? The key ideaShow
When objects are alike of one kind, alike of another and so on, objects have arrangements. To keep alike objects together, glue them into one block, which has one order inside.
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. Count the letters. A four times, L twice, H, B and D once each.
Step 2. All arrangements. .
Step 3. Glue the A's. The block and L, L, H, B, D make units, with L twice.
Step 4. Arrange the units. . The A's are alike, so the block adds no factor.
Answer: arrangements, and with the A's together.
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