Four people are to be selected to receive a modeling

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

Four people are to be selected to receive a modeling

by VJesus12 » Sat Feb 17, 2018 7:47 am

Four people are to be selected to receive a modeling contract from a group of 10 men, 5 women and 2 children. How many ways are possible in which 2 men, one woman and one child will receive a contract?

A. 90
B. 180
C. 225
D. 450
E. 900

The OA is the option D.

What is the best approach to solving this PS question? Is there a fast and easy way? I'd be thankful for your help experts.

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Source: Beat The GMAT — Problem Solving | Sat Feb 17, 2018 7:47 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » Sat Feb 17, 2018 8:50 am

VJesus12 wrote:Four people are to be selected to receive a modeling contract from a group of 10 men, 5 women and 2 children. How many ways are possible in which 2 men, one woman and one child will receive a contract?

A. 90
B. 180
C. 225
D. 450
E. 900

The OA is the option D.

What is the best approach to solving this PS question? Is there a fast and easy way? I'd be thankful for your help experts.

Hello Vjesus12.

Let's take a look at your question.

We have to select 2 men from 10 (10C2), one woman form 5 (5C2) and one child form 2 (2C1). Hence, the number of ways is $$10C\ 2=\frac{10!}{8!\cdot2!}=\frac{10\cdot9\cdot8!}{8!\cdot2}=\frac{90}{2}=45$$ $$5C\ 1=\frac{5!}{4!\cdot1!}=\frac{5\cdot4!}{4!}=5$$ $$2C\ 1=\frac{2!}{1!\cdot1!}=2$$

Hence, the final answer is 45*5*2=450.

Therefore, the correct answer is the option D.

I hope this answer may help you.

I'm available if you'd like a follow-up.

Regards.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

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GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Sat Feb 17, 2018 10:12 am

Hi VJesus12,

We're told that 4 people are to be selected to receive a modeling contract from a group of 10 men, 5 women and 2 children. We're asked for the number of possible ways in which 2 men, one woman and one child will receive a contract. You can answer this question by using the Combination Formula three times (although you really just have to use it once).

Since we're choosing 2 men, 1 woman and 1 child from each of their respective groups, we have three calculations to perform:

Men = choose 2 from a group of 10 = 10!/2!8! = (10)(9)/(2)(1) = 45 sets of 2 men
Women = choose 1 from a group of 5 = that's 5 options (you could also write this as 5!/1!4! = 5/1 = 5)
Children = choose 1 from a group of 2 = that's 2 options (you could also write this as 2!/1!1! = 2/1 = 2)

To get the total number of possibilities, we have to multiply those 3 outcomes: (45)(5)(2) = 450

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Jun 23, 2019 10:24 am

VJesus12 wrote:Four people are to be selected to receive a modeling contract from a group of 10 men, 5 women and 2 children. How many ways are possible in which 2 men, one woman and one child will receive a contract?

A. 90
B. 180
C. 225
D. 450
E. 900

We are given that 4 people are to be selected for a modeling contract. We must determine, from 10 men, 5 women, and 2 children, the number of ways that 2 men, 1 woman, and 1 child will receive a contract.

The number of ways that 2 men will receive a contract is 10C2 = (10 x 9)/2! = 45.

The number of ways that 1 woman will receive a contract is 5C1 = 5.

The number of ways that 1 child will receive a contact is 2C1 = 2.

Thus, the number of ways such that 2 men, 1 woman, and 1 child will receive a contract is:

45 x 5 x 2 = 450

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]