Aptitude - Permutation and Combination - Discussion
Discussion Forum : Permutation and Combination - General Questions (Q.No. 8)
8.
In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
Answer: Option
Explanation:
| Required number of ways | = (8C5 x 10C6) | |||||||
| = (8C3 x 10C4) | ||||||||
|
||||||||
| = 11760. |
Discussion:
61 comments Page 2 of 7.
Charan said:
8 years ago
8c3 = 8!/3!*(8-3)! = 8!/3!*5! which is equal to 8c5 = 8!/5!*(8-5)! = 8!/5!*3!.
B S said:
8 years ago
The Answer should be 266.
Siri said:
9 years ago
@Toluwalase.
This doesn't talk about the arrangement. It talks about the selection.
This doesn't talk about the arrangement. It talks about the selection.
Toluwalase said:
9 years ago
Yeah, I think I get the second step of the solution. But why do we have to find the number of ways the others can be arranged. We were asked to find the number of ways 5 men could be gotten from a total of 8 men and how we can get 6 women from the total of 10 women to form the committee. So the answer is meant to be 266. Why the additional calculation? Please answer.
Rishu.R said:
9 years ago
Why the second step conversion is needed? Is it necessary?
How do I predict the 2nd step conversion from the question?
Anyone, please help me. In detail.
How do I predict the 2nd step conversion from the question?
Anyone, please help me. In detail.
Shiv said:
9 years ago
By nCr.
8C5 * 10C6 = (8 * 7 * 6 * 5 * 4/1 * 2 * 3 * 4 * 5)* (10 * 9 * 8 * 7 * 6 * 5 * 4/1 * 2 * 3 * 4 * 5 * 6),
= 56 * 210,
= 11760.
Similarly, nC (n-r).
8C3 * 10C5 = (8* 7 * 6/1 * 2 * 3) * (10 * 9 * 8 * 7/1 * 2 * 3 * 4),
= 56 * 210,
= 11760.
8C5 * 10C6 = (8 * 7 * 6 * 5 * 4/1 * 2 * 3 * 4 * 5)* (10 * 9 * 8 * 7 * 6 * 5 * 4/1 * 2 * 3 * 4 * 5 * 6),
= 56 * 210,
= 11760.
Similarly, nC (n-r).
8C3 * 10C5 = (8* 7 * 6/1 * 2 * 3) * (10 * 9 * 8 * 7/1 * 2 * 3 * 4),
= 56 * 210,
= 11760.
Akash said:
9 years ago
Apply permutation formula when the order in which you place the object doesn't matter.
Permutation formula is : nPr = n! / (n-r)! * r! .
This is what is simply done here.
Permutation formula is : nPr = n! / (n-r)! * r! .
This is what is simply done here.
Raghav said:
9 years ago
8C5 * 10C6 = 11760.
But an addition to this 11760 * 11!? Why is this missing?
But an addition to this 11760 * 11!? Why is this missing?
Tshering said:
9 years ago
@Ravi.
8C5 = (8 * 7 * 6* 5 * 4)/(5 * 4 * 3 * 2 * 1) = after cancelling 5 & 4, left with (8 * 7 *6 ) / (3 * 2* 1 ) which is same as 8C3.
8C3 = (8 * 7* 6 )/(3 * 2 * 1).
Another way of 8C5 coming to 8C3 is 8C5 = 8C(8-5) = 8C3.
8C5 = (8 * 7 * 6* 5 * 4)/(5 * 4 * 3 * 2 * 1) = after cancelling 5 & 4, left with (8 * 7 *6 ) / (3 * 2* 1 ) which is same as 8C3.
8C3 = (8 * 7* 6 )/(3 * 2 * 1).
Another way of 8C5 coming to 8C3 is 8C5 = 8C(8-5) = 8C3.
Ganganesh said:
9 years ago
Thank you all.
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