GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 16:15

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# There are five empty chairs in a row. If six men and four women are wa

Author Message
TAGS:

### Hide Tags

Senior RC Moderator
Joined: 02 Nov 2016
Posts: 4127
GPA: 3.39
There are five empty chairs in a row. If six men and four women are wa  [#permalink]

### Show Tags

Updated on: 18 Oct 2018, 14:23
5
00:00

Difficulty:

25% (medium)

Question Stats:

78% (02:36) correct 22% (02:24) wrong based on 125 sessions

### HideShow timer Statistics

There are five empty chairs in a row. If six men and four women are waiting to be seated, what is the probability that the seats will be occupied by two men and three women?

A) 4/21
B) 5/21
C) 8/21
D) 9/21
E) 11/21

Source: Platinum GMAT
Difficulty Level: Medium

_________________

Last edited by SajjadAhmad on 18 Oct 2018, 14:23, edited 1 time in total.
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4774
Location: India
GPA: 3.5
Re: There are five empty chairs in a row. If six men and four women are wa  [#permalink]

### Show Tags

14 Jan 2017, 08:39
Source: platinum gmat

There are five empty chairs in a row. If six men and four women are waiting to be seated, what is the probability that the seats will be occupied by two men and three women?

A) 4/21
B) 5/21
C) 8/21
D) 9/21
E) 11/21

$$\frac{(6C2 * 4C3)}{10C5} = \frac{5}{21}$$

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Intern
Status: in process
Joined: 18 Jun 2017
Posts: 30
Location: Uzbekistan
Schools: Babson '21
GMAT 1: 690 Q47 V37
GPA: 4
WE: Education (Education)
Re: There are five empty chairs in a row. If six men and four women are wa  [#permalink]

### Show Tags

23 Oct 2017, 18:19
Bunuel

can you please explain why in this case we do not multiply the 6C2 by 2? and 4C3 by 3?

is it not usually the case that if two men are seated together they can be seated either as 1M, 2M, or 2M or 1M?
Math Expert
Joined: 02 Sep 2009
Posts: 58445
Re: There are five empty chairs in a row. If six men and four women are wa  [#permalink]

### Show Tags

24 Oct 2017, 00:40
ILoveNargiza wrote:
Bunuel

can you please explain why in this case we do not multiply the 6C2 by 2? and 4C3 by 3?

is it not usually the case that if two men are seated together they can be seated either as 1M, 2M, or 2M or 1M?

First of all, I think you meant 2! and 3! not 2 and 3.

Next, we are not interested in their arrangements on chairs, we just want the seats to be occupied by two men and three women.
_________________
Manager
Joined: 23 Jul 2014
Posts: 81
Re: There are five empty chairs in a row. If six men and four women are wa  [#permalink]

### Show Tags

28 Aug 2018, 18:43
Bunuel wrote:
ILoveNargiza wrote:
Bunuel

can you please explain why in this case we do not multiply the 6C2 by 2? and 4C3 by 3?

is it not usually the case that if two men are seated together they can be seated either as 1M, 2M, or 2M or 1M?

First of all, I think you meant 2! and 3! not 2 and 3.

Next, we are not interested in their arrangements on chairs, we just want the seats to be occupied by two men and three women.

@ILoveNargiza
I actually, mistakenly, calculated the permutations (no. of arrangements) and I got it right. What I did was: [(6C2 * 4C3 * 5!)/ 10*9*8*7*6]

1. So, firstly, I think you meant - multiple by 5! and not 2! and 3! individually because we would permute among all people, not just among men and women, if we are to find the total possible arrangements.
2. Secondly, here is the thing, as long as you take the ratio of permutations to permutations or combinations to combinations, you should be fine. Of course, It is not recommended but if you happen to confuse one for the other, as long as you are calculating the same thing (arrangements or selections/combinations) in the numerator and denominator, the answer will be the same.

Manager
Joined: 01 Nov 2017
Posts: 95
GMAT 1: 700 Q50 V35
GMAT 2: 640 Q49 V28
GMAT 3: 680 Q47 V36
GMAT 4: 700 Q50 V35
GPA: 3.84
Re: There are five empty chairs in a row. If six men and four women are wa  [#permalink]

### Show Tags

28 Aug 2018, 20:33
Alternative way to solve this question where we do consider the order.

Let's talk about the first possible order

MMWWW

Then the probabilities of picking that specific order is as follows:

Re: There are five empty chairs in a row. If six men and four women are wa   [#permalink] 28 Aug 2018, 20:33
Display posts from previous: Sort by