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02 Dec 2024, 22:07
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
58% (02:49) correct
42%
(02:29)
wrong
based on 139
sessions
History
Date
Time
Result
Not Attempted Yet
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?
A. 4320
B. 8640
C. 151200
D. 12960
E. 2160
A. 4320
B. 8640
C. 151200
D. 12960
E. 2160
02 Dec 2024, 23:05
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To reach the goal: no vowel ever touches another vowel.
We can arrange X,B,C,F,G,H first, so we can get 6!.
Then, there are 7 spaces between each letter " (1)X(2)B(3)C(4)F(5)G(6)H(7) ", which are also the spaces for the remaining 3 vowels to fit in, and then we can get 7C3, but don't forget to consider the order of these vowels, so we need to time 3!.
The final formula would be 6!*7C3*3!, which is 151200, C.
We can arrange X,B,C,F,G,H first, so we can get 6!.
Then, there are 7 spaces between each letter " (1)X(2)B(3)C(4)F(5)G(6)H(7) ", which are also the spaces for the remaining 3 vowels to fit in, and then we can get 7C3, but don't forget to consider the order of these vowels, so we need to time 3!.
The final formula would be 6!*7C3*3!, which is 151200, C.
03 Dec 2024, 08:42
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total ways - all vowels together
A,X,B,O,C, E, F, G & h
= 9factorial - 3factorial
A,X,B,O,C, E, F, G & h
= 9factorial - 3factorial
