The number of ways in which five letters can be selected from the word DESTROY so as to include exactly 2 vowels?
A) 10
B) 20
C) 30
D) 40
E) 60
(Asked by Vivek)
Ask a GRE Question : Permutation and Combination
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b
its option A) accordin to me..
if the word shuld have exactly two vowels fix the two vowels in their
places..ie they can be selected in 1 way.. n select 3 letters from other 5 available consonants…
ie in 5c2 ways…
ie 10 ways…
but the two vowels can arrange among themselves in 2 ways.
5c3
well dhaval the question is nt abt permutating…its just selecting…u cn arrange two vowel in two ways but there is only 1 way of selecting them…
ya avinash.i think ur rite.thnks for letting me know my mistake.
Correct answer is A. Avinash explanation is correct.
E
its option A) accordin to me..
if the word shuld have exactly two vowels fix the two vowels in their
places..ie they can be selected in 1 way.. n select 3 letters from other 5 available consonants…
ie in 5c3 ways…
ie 10 ways…
Get your own gravatar by visiting gravatar.com d
a
The first thing we have to fix that it’s combination problem. NOT Permutation.
Its A.
I agree with A.
A
2C2 *5C3 ways =1*10=10 ways total
okay the way i seee this problem is this:
first of all chooose all the possible ways in which you can choose 5 out of 7 alphabets. That should be 7C5 which i think is 21. Now let us think of all the choices in which both the vowels will not appear. Essentially then we have 5 alphabets and we have to choose 5 out of them (all of the consonants or the non-vowel alphabets). There is just one way to do it. So subtract it from all the possible choices. We get 21 -1 = 20. Option (B).
any comment is welcome
I think it’s B….
Here is my take:
There are 7P5 ways of chosing 5 letters out of 7. or 7!/2!=2520
However, this number includes those that have exactly 2 vowels left out. Number of cases when 2 vowels could be left out is 7P2, or 7!/5!=42
2520/42=60. Answer is 3
The formula for the future: = 7P5/7P2
This is not a computation problem, because order does matter.
thanks
5 choose 3 = 20
reason:we have DESTORY. 7 distinct letters, 2 vowels, 5 non-vowels.
They want 5 letter with 2 vowels and 3 non-vowels. What they really mean is want 3 non-vowels from the 5 non-vowels. That is, the answer is 5 choose 3 = 20.
ohh take gre team please help us in finding the answer
For Yami ::
The letters A, E, I, O, U are considered to be vowels; the remaining letters are considered to be consonants. However, Y is very frequently used as a vowel, and W may occasionally function as a vowel as well.
It is 2C2 * 5C3 = 20