Probability Help

Expert replies

kenyan_sun: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Sun Jan 13, 2008 6:54 pm

by kenyan_sun » Mon Feb 11, 2008 5:47 am

Hi,
Can someone please explain to me the 'C' in probability. How do i calculate the number of different ways 5 students and 2 teachers can be arranged for example.
Secondly, is there another letter (i think its P. but i could be wrong) that i need to be aware about.

Thanks in advance.

Cheers

Like this post

Source: Beat The GMAT — Problem Solving | Mon Feb 11, 2008 5:47 am

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Mon Feb 11, 2008 4:36 pm

"C" and "P" stand for combinations and permutations, which are different concepts than probability (although sometimes the concepts overlap on specific questions).

We use the combinations formula when we're counting unordered subgroups. If we have n total items and we want to know how many different subgroups of k items we can make, the formula is:

n!/k!(n-k)!

Quite often combinations are expressed with a big C and we'd say:

nCk.

We use the permutations formula when we're counting ordered subgroups. If we have n total distinct items and we want to know how many different ways we can arrange k of them, the formula is:

n!/(n-k)!

Quite often permutations are expressed with a big P and we'd say:

nPk.

In a simple situation where you're arranging n distinct items, the total number of possible permutations is n!.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course

Like this post

wreelp: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Thu Feb 07, 2008 4:49 pm; Location: Pittsburgh PA

Is the Answer 10?

by wreelp » Fri Feb 22, 2008 2:51 pm

I wrote out my quick calculation but i dont want to write it out and confuse you unless its correct...

Justin R Miller

Like this post

shwetonline: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Sun Feb 24, 2008 7:48 am

i think the answer is 21

by shwetonline » Sun Feb 24, 2008 9:49 am

According to my understanding,

We have to find out the permutation of 5 student & 2 teacher taken together. i.e. 7!

But we have to exclude the nternal permutation of 5 students & 2 teachers

i.e.

7!/(5!*2!) = 21

Please correct me if I am wrong.

Thanks,
Shweta

starting GMAT preparation

Like this post

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

Re: i think the answer is 21

by Stuart@KaplanGMAT » Sun Feb 24, 2008 10:26 am

shwetonline wrote:According to my understanding,

We have to find out the permutation of 5 student & 2 teacher taken together. i.e. 7!

But we have to exclude the nternal permutation of 5 students & 2 teachers

i.e.

7!/(5!*2!) = 21

Please correct me if I am wrong.

Thanks,
Shweta

We actually need more information before we can answer the question.

If we just care about where the "T"s and "S"s go in our arrangement, then your solution is 100% correct.

The generic formula for permutations in which we have non-distinct items is:

n!/r!s!t!...

where n is the total number of objects and r, s and t represent duplicates.

On the GMAT, this issue arises frequently in word jumble questions.

For example:

How many different ways are there to arrange the letters of the word "DESERT"?

n=6 and r=2 (two "E"s), so 6!/2!

How many different ways are there to arrange the letters of the word "DESSERT"?

n=7, r=2 (Es), s=2 (Ss), so 7!/2!2!

How many different ways are there to arrange the letters of the word "DESSERTS"?

n=8, r=2 (Es), s=3 (Ss), so 8!/2!3!

* * *

However, if each teacher and student is distinct and we care about where we put each individual person, the answer would simply be 7!=5040.

Like this post

wreelp: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Thu Feb 07, 2008 4:49 pm; Location: Pittsburgh PA

Number of ways

by wreelp » Sun Feb 24, 2008 4:53 pm

hello, now unless im missing something, there are 2 events (1. students and 2. teachers)
there are 5 possibilities for event 1 (students) and 2 possibilities for event 2 (teachers). So in order to calculate the number of possibilities for 1 student and 1 teacher, you just need to multiply the possibilities for each event.

so you have 5 x 2 = 10

10 different ways one student and one teacher can be arranged.

Justin R Miller

Like this post

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

Re: Number of ways

by Stuart@KaplanGMAT » Sun Feb 24, 2008 7:43 pm

wreelp wrote:hello, now unless im missing something, there are 2 events (1. students and 2. teachers)
there are 5 possibilities for event 1 (students) and 2 possibilities for event 2 (teachers). So in order to calculate the number of possibilities for 1 student and 1 teacher, you just need to multiply the possibilities for each event.

so you have 5 x 2 = 10

10 different ways one student and one teacher can be arranged.

"Arrange" means we care about order, which means permutations.

You solved a completely different question:

If you have 5 teachers and 2 students, how many different ways can you select 1 of each?

Like this post

humeixia: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Thu Apr 10, 2008 1:20 pm; Thanked: 1 times

by humeixia » Fri Apr 11, 2008 3:54 pm

thanks, stuart

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review