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Quantitative Reasoning – Practice – Is it probable; if yes, what are the chances!

PSA_PRACTICE_QNR48. A committee of seven members is to be formed from a group of 11 members. The probability that a certain married couple will either serve together or not at all is?

Ans:

Method 1:

Married couple serving in the seven members committee:

Number of ways to do this= Number of ways to select the couple * Number of ways in which 5 more people are selected from remaining 9 members
= 1*9c5
= 126

Married couple not serving in the seven members committee:

Consider selecting people to form the group of the people who are not forming the committee ( 4 members); if we are forming the non-committee members, rest of the members automatically form the committee

Number of ways to do this= Number of ways to select the couple in non-committee * Number of ways in which 2 more people are selected from remaining 11-2 or 9 members
= 1*9c2
= 26
Total probability= Total ways to select married couple in seven member committee or in the non-committee ‘group’ of 4 / Total ways to select 7 people out of 11

1*9c5 + 1*9c2
=——————
11c7

162
=——— = 81/165 = 27/55
330

Method 2:

Here, we try to select any one from the couple to form the committee and find out the probability. The required answer will be 1 minus this probability.

Number of ways of chosing any one from the Married couple serving in the seven members committee: 2c1
Number of ways of chosing rest 6 members for the 7 member-committee: 9c6 [It is 9c6 and not 10c6 as once any one member from the couple is selected the other one cannot be put back into the group of remaining people (needs to be excluded)].
Probability to form the committee where any one from the couple is chosen = 2*9c6/11c7
Required probability :

=1- 2*9c6/11c7
=1- 2*84/330
=1- 28/55
=27/55

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