Aptitude - Permutation and Combination - Discussion
Discussion Forum : Permutation and Combination - General Questions (Q.No. 1)
1.
From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
Answer: Option
Explanation:
We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).
 Required number of ways |
= (7C3 x 6C2) + (7C4 x 6C1) + (7C5) | |||||||||||
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||||||||||||
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||||||||||||
| = (525 + 210 + 21) | ||||||||||||
| = 756. |
Discussion:
137 comments Page 5 of 14.
Cyrus said:
1 decade ago
nCr = nCn-r
i.e n!/(r!*(n-r)!)
So, 7C4 = 7!/(4!*(7-4)!)
= 7*6*5*4*3*2*1/(4*3*2*1*(3*2*1))
= 7*6*5/3*2
= 35.
i.e n!/(r!*(n-r)!)
So, 7C4 = 7!/(4!*(7-4)!)
= 7*6*5*4*3*2*1/(4*3*2*1*(3*2*1))
= 7*6*5/3*2
= 35.
Shiva said:
1 decade ago
How do you find weather give problem can solved by combinations or permutation?
Anshul Vyas said:
1 decade ago
Mr. Mohan is absolutely right.
We know that 7c3 is not equal to 7c1*6c1*5c1.
In the same way we can't write 10c2 for rest two members.
We know that 7c3 is not equal to 7c1*6c1*5c1.
In the same way we can't write 10c2 for rest two members.
Ankz said:
1 decade ago
I think nikhil's query still not answered
Why would the logic 7C3 * 10C2 not work? First we've choosen 3 Men - 7C3. Now we have 10 people left (which included both men and women). Then we need to select any 2 people either men or women so 10C2. Please Clarify.
Anyone please elaborate whats wrong in this approach ?
Why would the logic 7C3 * 10C2 not work? First we've choosen 3 Men - 7C3. Now we have 10 people left (which included both men and women). Then we need to select any 2 people either men or women so 10C2. Please Clarify.
Anyone please elaborate whats wrong in this approach ?
Miguel said:
1 decade ago
If nCr=nCn-r, then why isn't 7c3 (from 7c3 x 6c2) changed to 7c4?
Abhishek said:
1 decade ago
Is any shortcut solution of above question?
Rishi said:
1 decade ago
How 7c3= 35 ?
Randika said:
1 decade ago
What is meant by nCr=nCn-r ?
Divya said:
1 decade ago
May be 5 womans is also possible, why we don't take that option?
Dipak said:
1 decade ago
@divya because there is a condition that, 3 man's are compulsory has to be select..
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