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?
Answer: Option
Explanation:
Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
| = (7C3 x 4C2) | |||||||||
|
|||||||||
| = 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 3 of 7.
Samiksha said:
1 decade ago
@Ridsie.
Let the no. of Re. 1 coin be x.
==>no. of 25 paise coins = x+1.33 x = 2.33 x.
==>no. of 50 paise coins = 105-(x+2.33 x) = 105-3.33 x.
(1)x+(25*2.33 x)/60+(50*(105-3.33 x))/60 = 50.50.
Solve for x.
Let the no. of Re. 1 coin be x.
==>no. of 25 paise coins = x+1.33 x = 2.33 x.
==>no. of 50 paise coins = 105-(x+2.33 x) = 105-3.33 x.
(1)x+(25*2.33 x)/60+(50*(105-3.33 x))/60 = 50.50.
Solve for x.
Sandhya said:
9 years ago
3 out of 7 consonants,
7 * 6 * 5/3 * 2 * 1 = 210/6
2 out of 4 vowels 4 * 3/2 * 1 = 12/2 = 6,
210/6 * 6 = 210.
Formation of 3 Consonants and 2 vowels 3 + 2 = 5.
5 * 4 * 3 * 2 * 1 = 120,
210 * 120 = 25200.
7 * 6 * 5/3 * 2 * 1 = 210/6
2 out of 4 vowels 4 * 3/2 * 1 = 12/2 = 6,
210/6 * 6 = 210.
Formation of 3 Consonants and 2 vowels 3 + 2 = 5.
5 * 4 * 3 * 2 * 1 = 120,
210 * 120 = 25200.
Athar said:
1 decade ago
You have to arrange the letter.
3 consonants out of 7.
2 vowels out of 4.
7c3x4c2 = 210.
You can do,
How many letter out of these letters?
3+2 = 5.
Now the required no of ways = 210 x 5!
3 consonants out of 7.
2 vowels out of 4.
7c3x4c2 = 210.
You can do,
How many letter out of these letters?
3+2 = 5.
Now the required no of ways = 210 x 5!
Adithya UN said:
8 years ago
Here, the answer is 302400.
Because you should 3 constants from 7 and 2 vowels from 4 and multiply then the answer is (7*6*5) * (4*3).
Later you should arrange them by multiplying with 5!.
Because you should 3 constants from 7 and 2 vowels from 4 and multiply then the answer is (7*6*5) * (4*3).
Later you should arrange them by multiplying with 5!.
Neha said:
1 decade ago
Why we multiply with 5! I cant understand. If we multiply with 5! in words then why we not multiply in persons it will also formed in different manner. Please someone explain this.
Prasant said:
1 decade ago
Finally multiplied with 5!, because, each word is consisted of 5 distinct letters. Had it been persons in place on letters, then 5! multiplication would not have been applied.
Harsha said:
1 decade ago
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 !
Why does the method differ here !
Mahima said:
9 years ago
Why can't we use permutation here instead of combination and multiplication by arrangement?
Since permutation = combination * arrangement.
But the answer is coming 2520.
Since permutation = combination * arrangement.
But the answer is coming 2520.
Student said:
1 decade ago
Can't we apply permutation directly here since in this question arrangement of words is to be done. i.e.
7P3*4P2 = 2520
One zero less to match the answer of 25200 :(
7P3*4P2 = 2520
One zero less to match the answer of 25200 :(
Ankita said:
8 years ago
@Himatheja.
We have to make word from both consonants and vowel that's why we have to multiply combination of consonants with vowel also,
7c3*4c2.
= 35*6.
= 210.
We have to make word from both consonants and vowel that's why we have to multiply combination of consonants with vowel also,
7c3*4c2.
= 35*6.
= 210.
(1)
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