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 GMAT 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.
It appears that you are browsing the GMAT Club forum unregistered!
Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club
Registration gives you:
Tests
Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.
Applicant Stats
View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more
Books/Downloads
Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!
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:
Re: In how many ways can 5 identical black balls and 7 identical [#permalink]
22 Oct 2005, 11:18
1
This post received KUDOS
1
This post was BOOKMARKED
fresinha12 wrote:
8C3? or 8C5?
gsr wrote:
A) 8C3 = 56
8C3 = 8C5
Position of white balls is fixed. Since they are identical, number of ways to arrange them is 1.
We have 6 spaces in btw the white balls and 1 each to the left and right end to accomodate the black ball. So 8 places in total to arrange 5 balls
8C5 (or 8C3)
Re: In how many ways can 5 identical black balls and 7 identical [#permalink]
23 Oct 2005, 07:24
there are 8 spaces availale so that no two black balls are together. that means 8! arrangements. but there are 5 identical black balls and 3 identical spaces. that`s why we have to divide by 5! and 3!. 8!/(5!3!). _________________
If your mind can conceive it and your heart can believe it, have faith that you can achieve it.
Re: In how many ways can 5 identical black balls and 7 identical [#permalink]
21 Jun 2015, 06:39
Hello from the GMAT Club BumpBot!
Thanks to another GMAT 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. _________________
In how many ways can 5 identical black balls and 7 identical [#permalink]
21 Jun 2015, 10:56
roopika2990 wrote:
Can anyone help me with this? I have no idea how to solve this.
Consider the possible arrangements:
WBWBWBWBWBWW or BWBWBWBWBWWW or WWBWBWBWBWBW or WWWBWBWBWBWB
Clearly, we are concerned about not placing 2 B's together, whites can be placed however we want.
So, it is like _W_W_W_W_W_W_W_ where black ball can be placed anywhere on the blank spaces, and this way, there never will be a case where 2 black balls fall together.
As there are 8 black spaces where 5 black balls can be placed, thus, the combination turns out as 8C5 (again, we are not concerned about the placement of white balls as we have already "fixed" their positions in the diagram above)
Also, we achieved at 8C5 as arranging 5 black balls on 8 different spots => 8!/5!3! (Total combination of available spaces = 8!; choosing 5 spaces out of them = 5!, arranging 3 leftover spaces = 3!) = 56
Re: In how many ways can 5 identical black balls and 7 identical [#permalink]
27 Jul 2015, 09:07
King407 wrote:
roopika2990 wrote:
Can anyone help me with this? I have no idea how to solve this.
Consider the possible arrangements:
WBWBWBWBWBWW or BWBWBWBWBWWW or WWBWBWBWBWBW or WWWBWBWBWBWB
Clearly, we are concerned about not placing 2 B's together, whites can be placed however we want.
So, it is like _W_W_W_W_W_W_W_ where black ball can be placed anywhere on the blank spaces, and this way, there never will be a case where 2 black balls fall together.
As there are 8 black spaces where 5 black balls can be placed, thus, the combination turns out as 8C5 (again, we are not concerned about the placement of white balls as we have already "fixed" their positions in the diagram above)
Also, we achieved at 8C5 as arranging 5 black balls on 8 different spots => 8!/5!3! (Total combination of available spaces = 8!; choosing 5 spaces out of them = 5!, arranging 3 leftover spaces = 3!) = 56
Hence answer is A
Hi King407, Can you elaborate how there is 8 places although there are 5 black balls? I do not get it
don't we consider here arranging 7 white balls in 7 places as 7!
so that num of ways can 5 identical black balls and 7 identical white balls be arranged in a row so that no 2 black balls are together is 7!*56 _________________
The path is long, but self-surrender makes it short; the way is difficult, but perfect trust makes it easy.
don't we consider here arranging 7 white balls in 7 places as 7!
so that num of ways can 5 identical black balls and 7 identical white balls be arranged in a row so that no 2 black balls are together is 7!*56
Hi, since the balls are identical, all 7 balls can be arranged at 7 places only in one way... yes had the ball been not identical, there would have been 7! ways _________________
As I’m halfway through my second year now, graduation is now rapidly approaching. I’ve neglected this blog in the last year, mainly because I felt I didn’...
Hilary Term has only started and we can feel the heat already. The two weeks have been packed with activities and submissions, giving a peek into what will follow...
Ninety-five percent of the Full-Time Class of 2015 received an offer by three months post-graduation, as reported today by Kellogg’s Career Management Center(CMC). Kellogg also saw an increase...