Free Practice Question
PS · Problem Solving
705-805
Combinations
In how many ways can the letters A,X,B,O,C, E, F, G and H be arranged such that no vowel ever touches another vowel?
Answer Choices
Correct answer marked belowA
4320
B
8640
151200
Correct
D
12960
E
2160
See the full step-by-step explanation
You can see the correct answer above. Sign in for free to unlock the complete worked solution.
Track your performance and improve
Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.
Explanation
Preview
Official Explanation
Official
To reach the goal: no vowel ever touches another vowel.
We can arrange X,B,C,F,G,H first, so we get .
Then, there are 7 spaces between each letter: (1)X(2)B(3)C(4)F(5)G(6)H(7), which are the spaces for the remaining 3 vowels to fit in, giving .…
We can arrange X,B,C,F,G,H first, so we get .
Then, there are 7 spaces between each letter: (1)X(2)B(3)C(4)F(5)G(6)H(7), which are the spaces for the remaining 3 vowels to fit in, giving .…
Read the full explanation
Sign in for free to see the complete step-by-step solution to this question.
Comments
Sign in to join the discussion
No comments yet
Be the first to share your thoughts and help others understand it better.
Sign in to commentWhat this question tests
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