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Aptitude - Permutation and Combination - Discussion

Discussion Forum : Permutation and Combination - General Questions (Q.No. 1)
Permutation and Combination
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?
564
645
735
756
None of these
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)
= 7 x 6 x 5 x 6 x 5 + (7C3 x 6C1) + (7C2)
3 x 2 x 1 2 x 1
= 525 + 7 x 6 x 5 x 6 + 7 x 6
3 x 2 x 1 2 x 1
= (525 + 210 + 21)
= 756.

Discussion:
137 comments Page 4 of 14.
Rajeev said:   1 decade ago
In the first step 7c5 converted 7c2 in the second step. But how ?
Renuka said:   1 decade ago
Because nCr = nCn-r.
Kumamako said:   1 decade ago
I think that it should be 3*2^3*3-3
Lana said:   1 decade ago
Hey can any one explain me how 210 came because I got 140 instead of 210.

Lookin forward for your support.
Osei-tutu said:   1 decade ago
Please what is mean by 7C3. Please help.
Kranthi said:   1 decade ago
How 7C4 became 7C3 ?
Siva said:   1 decade ago
7c4 = 7c(7-3)

So came 7c3 @kranthi...

Based on the formula nCr = nC(n-r).
Leo said:   1 decade ago
--> (7C3 x 6C2) + (7C4 x 6C1) + (7C5)

Shouldn't it be like this? --> (7C3 x 6C2) x (7C4 x 6C1) x (7C5)
Vivacity said:   1 decade ago
@leo: It can be A or B or C. The basic rules of permutations so we have to add them up A+B+C...where A,B,C refers to the terms.
Kanchan Srivastava said:   1 decade ago
nCr = nCn-r
and
7c4 = 35,
6c2= 15
I am unable to get it and how came
7c4 = 35 or 6c2= 15
Please explain it.
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