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Combinatorics problem:

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by Anurag@Gurome » Tue Jan 08, 2013 2:32 am
'manpreet singh wrote:Image
Casey should go 5 block down and 4 block left to travel exactly 9 blocks (DDDDDLLLL).
Required no. of days = 9!/(5!)(4!) = (9 * 8 * 7 * 6)/(4 * 3 * 2) = 3 * 7 * 6 = 126
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by The Iceman » Tue Jan 08, 2013 3:51 am
'manpreet singh wrote:Image
No matter what path she selects, she needs to go 4 times West and 5 times South.

Let's represent West by W and South by S. It is as good as arranging the letters of the 9-lettered word WWWWSSSSS. This is same as 9!/(5!*4!) = 9C5 = 9C4.

In general if there are m rows and n rows, the total number of ways is given by (m+n)Cm or (m+n)Cn

I have made and posted a video on this here: https://www.youtube.com/watch?v=A9x5Xf0mVXQ


We can also solve this easily by using Pascal's triangle and in fact even solve problems involving more complex grids. However, this is beyond the scope of the GMAT. If you wish to know more on this please go to a video that i prepared earlier.

https://www.youtube.com/watch?v=oSajgszc7y8
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by GMATGuruNY » Tue Jan 08, 2013 5:17 am
Check my posts here:

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by \'manpreet singh » Thu Jan 10, 2013 10:17 pm
Nice videos i must say.
Thanks you guys!

Br,
Manpreet Singh
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