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 7 of 7.
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! ?
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! ?
Pranay said:
1 decade ago
The question doesn't mention "distinct" consonants or vowels. So repetition should be allowed.
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 :(
Rahul said:
1 decade ago
@ Anil: The basic idea here is that first you pick out 3 consonants out of 7 and 2 vowels out of 4. Then you take the 5 letters that you have and make a word out of it. To pick out 3 consonants out of 7 you use the combination without repetition formula which states n!/(n-r)!r! which gives you 7C3 and the same for vowels gives you 4C2.
Once you have done that, you still need to make a word of it. You have 5 letters now that can be arranged into 5! ways to make a word so you multiply the three values since each step is dependent on the step before to make the final word. The answer comes out to be 35 x 6 x 120 respectively for each step mentioned chronologically.
Once you have done that, you still need to make a word of it. You have 5 letters now that can be arranged into 5! ways to make a word so you multiply the three values since each step is dependent on the step before to make the final word. The answer comes out to be 35 x 6 x 120 respectively for each step mentioned chronologically.
(1)
Anil said:
1 decade ago
Why multiply with 5?
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