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?
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 5 of 14.

Shams said:   1 decade ago
@Riya.

This is a Problem of Combination, There is only one formula is applied that is,
nCr = n!/(n-r)!r!.

(3 men and 2 women).

For man, n=7 & r=3.
For women n=6 & r=2.

(7C3 x 6C2) = 7! / (7-3)! 3! = 7*6*5*4*3! /4*3*2*1*3! = 840/24.

= 35.

So using this formula proceed further steps to get the result.

Sweety said:   1 decade ago
This method is ok but it will take much time to do in examination hall.

Swetha said:   1 decade ago
@Divya as in que asked as at least 3 men should be available in a group so we can't take 5 women. right?

Sharon said:   1 decade ago
GUYS.

How do we analyse that whether permutation or combination has to be used here?

H G said:   1 decade ago
Permutations are used to find the number of arrangements and combinations are you used to find the number of different ways of groups.

Rampal said:   1 decade ago
Ya because they said to select at least 3 men which means we can select till 5.

Shay tee said:   1 decade ago
Okay. How are 7c3 and 7c4 both equal to 35?

Chithra said:   1 decade ago
Combination is nothing but we are going to select from a particular group. In permutation also we will select from group, after selecting we need to arrange it according to the given condition.

i.e.) Combination -> selection.

Permutation -> selection followed by arrangement.

Krishan said:   1 decade ago
Anyone could explain why we used 7c2 in second step?

Priyanka Das said:   1 decade ago
7C2 means 2 men are selected from 7 men.


Post your comments here:

Your comments will be displayed after verification.