Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 18 Aug 2010
Posts: 83

In a high school debating team consisting of 2 freshmen, 2 sophomores, [#permalink]
Show Tags
17 Mar 2011, 06:33
Question Stats:
43% (01:25) correct 57% (01:10) wrong based on 69 sessions
HideShow timer Statistics
In a high school debating team consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors, two students are selected to represent the school at the state debating championship. The rules stipulate that the representatives must be from different grades, but otherwise the 2 representatives are to be chosen by lottery. What is the probability that the students selected will consist one freshman and one sophomore? A) 1/16 B) 1/8 C) 1/7 D) 1/6 E) 1/4 im not getting # of possible 2person groups PlZ help , thx Answer: Probability: 4/24 = 1/6
Official Answer and Stats are available only to registered users. Register/ Login.




Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1899

Re: In a high school debating team consisting of 2 freshmen, 2 sophomores, [#permalink]
Show Tags
17 Mar 2011, 07:04
Total number of ways to select 2 students from any two groups = \(C^4_2*C^2_1*C^2_1 = 4*(3/2)*2*2 = 24\) \(C^4_2\)  Number of ways to select 2 groups out of 4 groups \(C^2_1\)  Number of ways to select 1 student from 1 of the selected groups \(C^2_1\)  Number of ways to select 1 student from 2nd selected group There are total 24 ways in which you can select two students from any two groups. Selecting 2 students, one each from freshmen and sophomore = \(C^2_1*C^2_1=2*2=4\) P = 4/24 = 1/6.
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings




Director
Status: =Given to Fly=
Joined: 04 Jan 2011
Posts: 820
Location: India
Concentration: Leadership, Strategy
GMAT 1: 650 Q44 V37 GMAT 2: 710 Q48 V40 GMAT 3: 750 Q51 V40
GPA: 3.5
WE: Education (Education)

Re: In a high school debating team consisting of 2 freshmen, 2 sophomores, [#permalink]
Show Tags
17 Mar 2011, 07:10
Number of ways in which you can form a group of two where both are from same class is 4C1 = 4 Total number of ways in which a group of two can be formed is 8C2 = 28 Number of ways in which the group of two can be formed such that both are not from the same class are = 28  4 = 24 ways Number of ways of forming a group when one is a Sophomore and 1 is a Freshman is: 2C1 x 2C1 (One Sophomore AND One Freshman) = 2 x 2 = 4 Probability = 4/24 = 1/6
_________________
"Wherever you go, go with all your heart"  Confucius
Useful Threads
1. How to Review and Analyze your Mistakes (Post by BB at GMAT Club)
2. 4 Steps to Get the Most out out of your CATs (Manhattan GMAT Blog)
My Experience With GMAT
1. From 650 to 710 to 750  My Tryst With GMAT
2. Quest to do my Best  My GMAT Journey Log



Director
Status: =Given to Fly=
Joined: 04 Jan 2011
Posts: 820
Location: India
Concentration: Leadership, Strategy
GMAT 1: 650 Q44 V37 GMAT 2: 710 Q48 V40 GMAT 3: 750 Q51 V40
GPA: 3.5
WE: Education (Education)

Re: In a high school debating team consisting of 2 freshmen, 2 sophomores, [#permalink]
Show Tags
17 Mar 2011, 07:14



Manager
Joined: 18 Aug 2010
Posts: 83

Re: In a high school debating team consisting of 2 freshmen, 2 sophomores, [#permalink]
Show Tags
17 Mar 2011, 10:33
thx guys + kudos from me



Intern
Status: preparing
Joined: 30 Dec 2013
Posts: 41
Location: United Arab Emirates
Concentration: Technology, Entrepreneurship
GMAT 1: 660 Q45 V35 GMAT 2: 640 Q49 V28 GMAT 3: 640 Q49 V28 GMAT 4: 640 Q49 V28 GMAT 5: 640 Q49 V28
GPA: 2.84
WE: General Management (Consumer Products)

Re: In a high school debating team consisting of 2 freshmen, 2 sophomores, [#permalink]
Show Tags
18 Aug 2017, 03:06
f =2 , s=2 , j=2 and sn=2 total =8 students 2 are to be selected from 8 such that each is different.
total no. of ways to select 2 from 8= 8C2= 28 number of ways 2 are same = 4 (f,s,j,sn ) 284=24
selecting 1 freshman from 2, and 1 sophomore from 2 = (2C1 x 2C1)/24= 4/24 =1/6 ANS




Re: In a high school debating team consisting of 2 freshmen, 2 sophomores,
[#permalink]
18 Aug 2017, 03:06






