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A group of 4 persons is to be selected from 5 married couple

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A group of 4 persons is to be selected from 5 married couple

by BTGmoderatorDC » Fri Jan 18, 2019 4:29 am
A group of 4 persons is to be selected from 5 married couples, who are sitting in five different rows, A, B, C, D, and E. Each row can accommodate exactly one couple. If a person is selected from a row, which is marked by a vowel, then we need to select another person of opposite gender, from another row, which is also a vowel. In how many ways can the group be formed?

A. 15
B. 16
C. 60
D. 75
E. 76

OA E

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by swerve » Fri Jan 18, 2019 12:07 pm
We can have three cases to solve this question:

case 1: all 4 persons from non-vowel rows i.e 6 people
6c4: 15
case 2:
Given If a person is selected from a row, which is marked by a vowel, then we need to select another person of opposite gender, from another row, which is also a vowel.

so we have 2 males and 2 females ( row A & E)
we can say
2c1*2c1*6c2 = 60

case 3:

All people from A & E : 2c2*2c2 = 1

Total ways to form group 60+15+1= 76.
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