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October 10, 2023UGC NET CS 2015 Dec paper2
October 10, 2023UGC NET CS 2015 Dec paper2
Question 1

How many committees of five people can be chosen from 20 men and 12 women such that each committee contains at least three women?
75240


52492


41800


9900

Question 1 Explanation:
Given data,
— 20 men and 12 women
— 5 people can choose from men and women
— Each committee contains at least three women
Step1: We have a constraint that each committee contains atleast 3 women.
possibility1: 2 men + 3 women.
possibility2: 1 men + 4 women.
possibility3: 0 men + 5 women.
Step1: They are asking to find all possibilities.
= (possibility 1)+ (possibility 2) + (possibility 3)
= . ( ^{20} C_{ 2}. * ^{12} C_{ 3} ) + ( ^{20} C_{ 2}. * ^{12} C _{2} ) + ( ^{20} C_{ 2}. *^{ 12} C_{ 2} )
= (190*220) + (20*495) + (1*792)
= 41800 + 9900 + 792
= 52492
— 20 men and 12 women
— 5 people can choose from men and women
— Each committee contains at least three women
Step1: We have a constraint that each committee contains atleast 3 women.
possibility1: 2 men + 3 women.
possibility2: 1 men + 4 women.
possibility3: 0 men + 5 women.
Step1: They are asking to find all possibilities.
= (possibility 1)+ (possibility 2) + (possibility 3)
= . ( ^{20} C_{ 2}. * ^{12} C_{ 3} ) + ( ^{20} C_{ 2}. * ^{12} C _{2} ) + ( ^{20} C_{ 2}. *^{ 12} C_{ 2} )
= (190*220) + (20*495) + (1*792)
= 41800 + 9900 + 792
= 52492
Correct Answer: B
Question 1 Explanation:
Given data,
— 20 men and 12 women
— 5 people can choose from men and women
— Each committee contains at least three women
Step1: We have a constraint that each committee contains atleast 3 women.
possibility1: 2 men + 3 women.
possibility2: 1 men + 4 women.
possibility3: 0 men + 5 women.
Step1: They are asking to find all possibilities.
= (possibility 1)+ (possibility 2) + (possibility 3)
= . ( ^{20} C_{ 2}. * ^{12} C_{ 3} ) + ( ^{20} C_{ 2}. * ^{12} C _{2} ) + ( ^{20} C_{ 2}. *^{ 12} C_{ 2} )
= (190*220) + (20*495) + (1*792)
= 41800 + 9900 + 792
= 52492
— 20 men and 12 women
— 5 people can choose from men and women
— Each committee contains at least three women
Step1: We have a constraint that each committee contains atleast 3 women.
possibility1: 2 men + 3 women.
possibility2: 1 men + 4 women.
possibility3: 0 men + 5 women.
Step1: They are asking to find all possibilities.
= (possibility 1)+ (possibility 2) + (possibility 3)
= . ( ^{20} C_{ 2}. * ^{12} C_{ 3} ) + ( ^{20} C_{ 2}. * ^{12} C _{2} ) + ( ^{20} C_{ 2}. *^{ 12} C_{ 2} )
= (190*220) + (20*495) + (1*792)
= 41800 + 9900 + 792
= 52492
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