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21 Jun 2022, 12:45
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
66% (01:03) correct
34%
(01:05)
wrong
based on 103
sessions
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In how many ways can be letters of the word “DISCOVERY” be arranged so that the vowels are always together ?
A. 6!*3!
B. 7!*3!
C. 8!
D. 8!*3!
E. 8!*4!
A. 6!*3!
B. 7!*3!
C. 8!
D. 8!*3!
E. 8!*4!
21 Jun 2022, 13:11
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Bunuel
A, E, I, O, U and sometimes Y...in this case, Y is not a vowel!
Let's group the vowels together. How many ways are there to arrange just the three vowels? 3!
Okay, now let's consider the vowels as one element and each of the other six letters as an element. There are seven total elements. How many ways are there to arrange the seven elements? 7!
We need to arrange the seven elements and also have 3! ways to rearrange just the vowels within that, so there are 7!3! total ways.
Answer choice B.
21 Jun 2022, 17:28
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The answer would be 6!*3! instead of 7!*3! as the number of letters in "DISCOVERY" is 8 and if vowels are to occur together they will form 1 element and thus remaining 5 letters will form individual 5 elements. Thus total of 6 elements are to be arranged. Further, the 3 vowels could be arranged in 3! ways so 6!*3!
21 Jun 2022, 17:52
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This question I do partially by addiction principle and partially by permutation without repetition.
The author helped me putting the total quantity of letters as a multiple of the total quantity of vowels.
The author helped me putting the total quantity of letters as a multiple of the total quantity of vowels.
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