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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?

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

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)

= . (

= (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

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)

= . (

= (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

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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