GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 03 Jul 2020, 09:55

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

Six couples are invited to play a game of cards, which needs 4 players

Author Message
TAGS:

Hide Tags

Intern
Joined: 12 Feb 2020
Posts: 13
Six couples are invited to play a game of cards, which needs 4 players  [#permalink]

Show Tags

Updated on: 06 Jun 2020, 03:00
1
1
4
00:00

Difficulty:

45% (medium)

Question Stats:

62% (01:30) correct 38% (01:48) wrong based on 39 sessions

HideShow timer Statistics

Six couples are invited to play a game of cards, which needs 4 players at a time. In how many ways can the players be selected, if no couple should be included?

(A) 256
(B) 384
(C) 240
(D) 320
(E) 60

Originally posted by Keyurneema on 06 Jun 2020, 02:55.
Last edited by Bunuel on 06 Jun 2020, 03:00, edited 1 time in total.
Renamed the topic.
Intern
Joined: 06 Oct 2019
Posts: 14
Concentration: Strategy, Technology
WE: Marketing (Internet and New Media)
Six couples are invited to play a game of cards, which needs 4 players  [#permalink]

Show Tags

Updated on: 11 Jun 2020, 19:52
Six couples but no couple can play card game at a time. i.e. only a single person form each couple pair
Also, only 4 players can play the game at a time.

Step 1
We start with selecting 4 couples out of 6 couples. (Because only 4 players can play at one time.)

This is done in $$6C4$$ ways. ===> $$6C4 = 6!/(4!*2!)$$ = 15 ways.

Step 2
Now that we have selected the 4 couples, we select one from the pair who actually plays the card game.
(Because no couple should be included i.e. only one person from a couple pair can be selected)

4 couples, we can select 1 person from each pair. i.e. 2 choices per couple.
This is done is $$2^4$$ = $$2*2*2*2$$ = 16 ways.

Both conditions need to be satisfied, so it's an AND case of combination.
Total ways = 15*16 = 240 ways.

_________________
Your critical analysis of this post is appreciated and would help me reach 700+

Originally posted by Rajat8 on 06 Jun 2020, 06:26.
Last edited by Rajat8 on 11 Jun 2020, 19:52, edited 1 time in total.
Senior Manager
Joined: 10 Dec 2017
Posts: 270
Location: India
Re: Six couples are invited to play a game of cards, which needs 4 players  [#permalink]

Show Tags

06 Jun 2020, 07:07
1
Keyurneema wrote:
Six couples are invited to play a game of cards, which needs 4 players at a time. In how many ways can the players be selected, if no couple should be included?

(A) 256
(B) 384
(C) 240
(D) 320
(E) 60

Total cases= 12C4=495
Cases which are not required= 2 couples or 1 couple and 2 others(not couple)
2 couples= 6C2=15
1 couple + 2 others=6C1*(1*8C1*5)=240 ( after selecting one couple among 6, we are left with 5 couples. Now select anyone( 1 way), then we are left with 8 people as we can not select the his or her partner. And we can select 1 person among 8 people in 8C1 ways and we have 5 such couples. So 1*8C1*5)
Cases which are not required=255
Required cases=495-255
=240
C:)
Manager
Joined: 01 Nov 2017
Posts: 103
Location: India
Schools: ISB '21
GMAT 1: 690 Q49 V36
GPA: 4
WE: Web Development (Consulting)
Re: Six couples are invited to play a game of cards, which needs 4 players  [#permalink]

Show Tags

06 Jun 2020, 08:12

No couples allowed at one time, so one player from a couple can be selected at one time

$$=> 6C4 =\frac{ 6!}{(4! * 2!)} => 15 ways$$

Each player from a couple can be selected in 2 ways => either first or second and there are 4 couples so, $$2 ^ 4 = 16 ways$$

Total ways = $$15 * 16 = 240 ways$$ (C)
Intern
Joined: 12 Feb 2020
Posts: 13
Re: Six couples are invited to play a game of cards, which needs 4 players  [#permalink]

Show Tags

06 Jun 2020, 08:16
* Select 4 couple out of 6 couple- 6C4, & Than selecting 1 person from a couple because both can not Play together- 2 WAYS

=6C4*2*2*2*2= 15*16= 240

Ans -C
GMAT Tutor
Joined: 24 Jun 2008
Posts: 2276
Re: Six couples are invited to play a game of cards, which needs 4 players  [#permalink]

Show Tags

06 Jun 2020, 08:29
1
1
Imagine first we're picking a first player, second player, third player and fourth player. We'd have 12 choices for the first player, 10 for the second (to avoid picking a couple), 8 for the third and 6 for the fourth. So we'd have (12)(10)(8)(6) choices. But presumably the order of the 4 players is irrelevant, so we must divide by 4!, and we get

(12)(10)(8)(6)/(4!) = (5)(8)(6) = 240 possible selections
_________________
GMAT Tutor in Montreal

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 6416
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Six couples are invited to play a game of cards, which needs 4 players  [#permalink]

Show Tags

06 Jun 2020, 09:44
Keyurneema wrote:
Six couples are invited to play a game of cards, which needs 4 players at a time. In how many ways can the players be selected, if no couple should be included?

(A) 256
(B) 384
(C) 240
(D) 320
(E) 60

method 1
12*10*8*6/4! = 240
method 2
6c3*2*2*2*2 ; 15*16 ; 240
OPTION C
Re: Six couples are invited to play a game of cards, which needs 4 players   [#permalink] 06 Jun 2020, 09:44