Web-Technologies
October 10, 2023
UGC NET CS 2015 Dec- paper-2
October 10, 2023
Web-Technologies
October 10, 2023
UGC NET CS 2015 Dec- paper-2
October 10, 2023

UGC NET CS 2015 Dec- paper-2

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?
A
75240
B
52492
C
41800
D
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
Step-1: We have a constraint that each committee contains atleast 3 women.
possibility-1: 2 men + 3 women.
possibility-2: 1 men + 4 women.
possibility-3: 0 men + 5 women.
Step-1: 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
Step-1: We have a constraint that each committee contains atleast 3 women.
possibility-1: 2 men + 3 women.
possibility-2: 1 men + 4 women.
possibility-3: 0 men + 5 women.
Step-1: 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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