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 Your Progress
every week, we’ll send you an estimated GRE score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Your score will improve and your results will be more realistic
Is there something wrong with our timer?Let us know!
An equal number of juniors and seniors are trying out for
[#permalink]
05 Oct 2017, 20:38
2
Bookmarks
00:00
Question Stats:
59% (01:41) correct
40% (03:21) wrong based on 44 sessions
HideShow
timer Statistics
An equal number of juniors and seniors are trying out for six spots on the university debating team. If the team must consist of at least four seniors, then how many different possible debating teams can result if five juniors try out?
Re: An equal number of juniors and seniors are trying out for
[#permalink]
05 Oct 2017, 21:36
1
1
Bookmarks
Bunuel wrote:
An equal number of juniors and seniors are trying out for six spots on the university debating team. If the team must consist of at least four seniors, then how many different possible debating teams can result if five juniors try out?
(A) 50 (B) 55 (C) 75 (D) 100 (E) 250
Kudos for correct solution.
Here it is given as five juniors try out i.e we have 5 juniors and 5 seniors since equal number try out for the six spots
Now we can have two combination
first one - 4 seniors and 2 juniors = 5C4 * 5C2 =50 (We have to keep minimum nos of seniors to 4 as the statement says atleast 4 numbers of seniors are in the team)
Second one- 5 seniors and 1 juniors = 5C5 * 5C1 = 5
Re: An equal number of juniors and seniors are trying out for
[#permalink]
10 Jan 2019, 23:07
Expert Reply
For anyone who gets stumped by which way to use combinatorics, lets think about this.
First, They say that there are equal numbers of juniors and seniors, and there are 5 juniors, which means there are 5 seniors and a total of 10 players
Now, lets find the total number of all 6 team combinations out of 10 players, which is 10c6= 210, so it cant be greater than this number, which means we eliminate E
Its said that there are at least 4 seniors that must be on the team, which means that there are 4 out of 5 seniors that have to be picked, leaving only 2 out of 5 Juniors that can be picked after. picking 4 out of 5 seniors is 5c4, picking 2 out of 5 juniors is 5c2 thus 5c4*5c2= 5*10= 50
but what if 5 out of 5 seniors get picked? then 5c5=1 leaving only 1 out of 5 juniors to be picked, 5c1=5 Thus 5c5*5c1= 1*5=5
Re: An equal number of juniors and seniors are trying out for
[#permalink]
01 Aug 2020, 06:19
Bunuel wrote:
An equal number of juniors and seniors are trying out for six spots on the university debating team. If the team must consist of at least four seniors, then how many different possible debating teams can result if five juniors try out?
(A) 50 (B) 55 (C) 75 (D) 100 (E) 250
Kudos for correct solution.
If the team must have AT LEAST 4 seniors, then we must consider two possible cases: Case i: The team has 4 seniors and 2 juniors Case ii: The team has 5 seniors and 1 junior
Case i: The team has 4 seniors and 2 juniors Since the order in which we select the seniors does not matter, we can use combinations. STAGE 1: We can select 4 seniors from 5 seniors in 5C4 ways (= 5 ways) STAGE 2: We can select 2 juniors from 5 juniors in 5C2 ways (= 10 ways) By the Fundamental Counting Principle (FCP), we can complete both stages in (5)(10) ways = 50 ways
Aside: See the video below to learn how to quickly calculate combinations (like 5C2) in your head
Case ii: The team has 5 seniors and 1 junior STAGE 1: We can select 5 seniors from 5 seniors in 5C5 ways (= 1 way) STAGE 2: We can select 1 junior from 5 juniors in 5C1 ways (= 5 ways) By the Fundamental Counting Principle (FCP), we can complete both stages in (1)(5) ways = 5 ways
Re: An equal number of juniors and seniors are trying out for
[#permalink]
22 Jan 2022, 05:11
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
gmatclubot
Re: An equal number of juniors and seniors are trying out for [#permalink]
05 Oct 2017, 20:38 
59% (01:41) correct
