Aptitude - Permutation and Combination - Discussion

This cannot be a permutation problem because the first thing we ought to do is select 4 consonants out of 7 and 2 vowels out of 4.

Let us approach the question by assigning actual alphabets, and reducing the quantity. Suppose there are 3 consonants B, C and D and 2 vowels A and E, and we have to form a word using 2 consonants and 1 vowel.

The required words are: ABC, BAC, BCA, ACB, CAB, CBA, ACD, CAD, CDA, DCA, DAC, ADC.....the sum would be 36.

Let us now do the sum using formula:
3P2*2P1=12, which is clearly not the answer.

We can do this problem with permutation.

Let me explain.

We got 2520 by permutation but its not complete. It is only the permutation of two sets of alphabets. So what we have missed out is combining both the sets and the number of ways of combining the two sets (3c and 2v) is 10. So finally we get 25200 as the answer.

They are:
vvccc
vcvcc
vccvc
vcccv
cvvcc
cvcvc
cvccv
ccvvc
ccvcv
cccvv

When we apply permutation and combination? please tell me one.

Combination 3 consonant and 2 vowels is still left. By adding forms 5! and then rest to find the total.

How can we find the given problem is from permutation or combination?

Here we should use permutations we need to use combinations and just selecting the consonants and vowels from the given 7 consonants and 4 vowels, its not necessary to multiply with 120 there so according to me, its 210 just selecting those consonants and vowels from the given one not more than that.

@Harsha.

Here the asking question is group of words (use combination) not to asking about the order of words so don't use the permutation. OK.

When I saw this question I was like it will be permutation since arrangement of words is important and I did 7P3*4P2(just like other sums).

Why does the method differ here !

I don't know why all are confusing as permutation and combination.

I think this question"how many words can be FORMED " is clearly combination.

NO. It's not because of the letters (and not person) we should multiply with 5!, but it's about what the question said; how many words can be FORMED? that's we call PERMUTATION. At first we might have thought it's just COMBINATION because we didn't notice the last phrase of the question said how many words can be FORMED. So it's considered as both PERMUTATION and COMBINATION.