An office has 6 employees; there are 5 female employees and 1 male emp

Question

An office has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee?

A. 10
B. 12
C. 15
D. 24
E. 30

Total Employees: 6
Female: 5
Male: 1

committee of 3 with inclusion of Male

Number of ways Female can be selected : 5C2 = 10
For male it should be  6C1  or  6C6 
 6C1= 6
6C6= 1

OA = 10

hirendhanak · Answer

for male 1C1 = 1 ........ A
foe female = 5C2 = 10.........B

total = 10*1
= 10 - answer

saurabhgoel · Answer

I also got Answer as - 10

Bunuel · Answer

C^2_5*C^1_1=10 : there is only ONE male employee, so # of ways to choose 1 out of 1 is  C^1_1=1 , # of ways to choose 2 other members from 5 women is  C^2_5 .

adkikani · Answer

Hi  chetan2u   EMPOWERgmatRichC   GMATPrepNow   VeritasKarishma   Bunuel

Can you point out why did I falter solving this question using Fundamental counting principle?

I have to fill 3 places:
Place 1: I like to use restrictions first. Can be filled by the only male, 1 male to choose from for 1 slot, or 1C1 = 1
Place 2: 5 females to choose from , for second slot , 5C1 ie 5
Place 3: 4 female to choose from , for third slot . 4C1 ie 4

Total no of arrangements = 4*5 = 20

chetan2u · Answer

After choosing 1 male, you have got into ARRANGEMENTS, 5*4, while the question is about SELECTION, 5C2.

SO, 5*4 contains 2 different arrangements where a,b is different from b,a. Thus, divide your answer by 2---20/2=10

EMPOWERgmatRichC · Answer

Hi adkikani,

We're told that an office has 6 employees (5 female employees and 1 male employee). We're asked for the number of ways that a 3-person committee can be created if the committee must include the male employee. This question can be treated as either a Permutation OR a Combination (depending on how you want to do the math). In addition, since the number of options is relatively small, you could 'brute force' the solution by writing out all of the possibilities.

Since we're forming a 'group', the order of the 3 people does NOT matter. Thus, using the Combination Formula would make sense. The one male employee would take that one 'spot', leaving the 5 female employees for the remaining 2 spots.... 5c2 = (5!)/(2!)(3!) = (5)(4)/(2)(1) = 10 possible groups.

After placing the one male employee, you could do the rest of the calculation as a Permutation. However, you have to realize that a Permutation will create "duplicate" groups - and we will have to remove those duplicates.

5 women for the 1st spot
4 women for the 2nd spot
(1)(5)(4) = 20.... however, each group in there has been counted twice (since the pair A,B is the same as the pair B,A). Thus, we have to divide this total by 2... 20/2 = 10 groups.

Final Answer:  A

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

beyyaar · Answer

We are told that the total employees in an office is 6 of which 5 are females and 1 is male.

We are asked to make a committee of 3 and it should include a male.

Now from the total employees, there is only 1 male and as in committee selection the order does not matter as there is no designation here, we can select any one spot for the male. So the number of ways to choose for a male is 1C1 = 1.

For the remaining two spots, we got to choose 2 from 5 females, the number of ways females can be chosen is 5C2=10. 
Total number of ways committee can be made is 10*1=10.

BrentGMATPrepNow · Answer

In order to ensure that the 3-person committee includes the male employee, we'll start by placing the male employee on the committee. 
Our task now is to choose 2 more people (from the 5 female employees) to join the male on the committee.

Since the order in which we select the two people does not matter, we can use combinations. 
We can select 2 employees from 5 employees in 5C2 ways (= 10 ways)

Answer: A

Cheers,
Brent

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

An office has 6 employees; there are 5 female employees and 1 male emp

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

An office has 6 employees; there are 5 female employees and 1 male emp

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards