Free Practice Question
PS · Problem Solving
705-805
Combinations
In how many ways can letters the word ATTITUDE be rearranged such that no two Ts are adjacent to each other?
Answer Choices
Correct answer marked belowA
1800
2400
Correct
C
3600
D
4320
E
6720
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Explanation
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Official Explanation
Official
Without the Ts, there are 5 other distinct letters: A, I, U, D, E.
These 5 letters can arrange themselves in or 120 ways.
To ensure that no two Ts are together, there must be at least one letter between any two Ts.
If we represent each of the other letters as X, then the arrangement can be _X_X_X_X_X_…
These 5 letters can arrange themselves in or 120 ways.
To ensure that no two Ts are together, there must be at least one letter between any two Ts.
If we represent each of the other letters as X, then the arrangement can be _X_X_X_X_X_…
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What it tests
Whether you can count arrangements and selections correctly — permutations vs. combinations.
Common trap
Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.
Details
Difficulty
705-805
Type
PS
Category