Aptitude - Permutation and Combination - Discussion

Discussion Forum : Permutation and Combination - General Questions (Q.No. 4)
4.
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
210
1050
25200
21400
None of these
Answer: Option
Explanation:

Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)

      = (7C3 x 4C2)
= 7 x 6 x 5 x 4 x 3
3 x 2 x 1 2 x 1
= 210.

Number of groups, each having 3 consonants and 2 vowels = 210.

Each group contains 5 letters.

Number of ways of arranging
5 letters among themselves
= 5!
= 5 x 4 x 3 x 2 x 1
= 120.

Required number of ways = (210 x 120) = 25200.

Video Explanation: https://youtu.be/dm-8T8Si5lg

Discussion:
65 comments Page 4 of 7.

Neeraj Tailor said:   8 years ago
How many numbers greater than 5000 can be formed with the digits, 3, 5, 7, 8, 9 no digit being repeated?

In this question we won't multiply instead of adding?

M.V.KRISHNA/PALVONCHA said:   1 decade ago
Hi suchi.

Given 3c out of 7c

2v out of 4v.

So, required number of letters are 5. they can be arranged among

themselves in 5!.

Hope you understood.

Soumyajit said:   3 years ago
This question mentions it 7C3=> 7x6x5x4/6.
7x5x4.
= > 35x4,
= > 140,
= > 140 x 6x 120,
= > 140x 720 ways.
= > 100800 ways.
(3)

Aadesh said:   8 years ago
I agree @Ankita.

That as we are picking up the words by applying combination means that we are forming the words therefore answer. It Should be 210.
(1)

Rizwana said:   1 decade ago
Hi,

I always find problem in using C and P in formula I could not distinguish when to use nCr and when to use nPr please help in finding difference.

Shub said:   1 decade ago
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.

Shams said:   1 decade ago
@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.

Suchi said:   1 decade ago
c = consonants
v = vowels

Why has the num of letters has to be 5?

Can't it be 4c+3v(7 letter) or 5c+4v(9 letters)

Then how can v take 5! ?

Navin said:   1 decade ago
Hey they anly asked us how many ways to form the letters they didint ask how many ways to arrange it the answer is wrong it should be 210.

Ajay said:   1 decade ago
Can anyone help me to understand when have to take NCR or when have to take NPR in easily manner. I am more confused about this concept.


Post your comments here:

Your comments will be displayed after verification.