http://betterexplained.com/articles/navigate-a-grid-using-combinations-and-permutations/ Learning shouldn't hurt. Let's share the insights that made difficult ideas click. Wed, 08 Sep 2010 10:32:31 +0000 http://wordpress.org/?v=2.8.4 hourly 1 http://betterexplained.com/articles/navigate-a-grid-using-combinations-and-permutations/#comment-284735 Kalid Sun, 09 May 2010 06:36:33 +0000 http://betterexplained.com/?p=205#comment-284735 @Dud: Thanks! Yes, Pascal's Triangle is another cool way to see it. @Dud: Thanks! Yes, Pascal’s Triangle is another cool way to see it.

]]> http://betterexplained.com/articles/navigate-a-grid-using-combinations-and-permutations/#comment-283533 Dud Thu, 06 May 2010 12:38:21 +0000 http://betterexplained.com/?p=205#comment-283533 Another solution is using Pascal's triangle (and by extension, the binomial theorem) If you consider the number of ways you can reach successive corners, Pascal's forms from the start up toward the finish. Another solution is using Pascal’s triangle (and by extension, the binomial theorem) If you consider the number of ways you can reach successive corners, Pascal’s forms from the start up toward the finish.

]]> http://betterexplained.com/articles/navigate-a-grid-using-combinations-and-permutations/#comment-270614 Matt Wed, 20 Jan 2010 03:32:50 +0000 http://betterexplained.com/?p=205#comment-270614 In the random walk problem, is the number of possible up/right steps really 2^10? If we randomly pick either 'up' or 'right' ten times, then we will get some paths that take us beyond the boundaries of the grid like 10 consecutive up movements or 10 consecutive right movements. Since these are impossible, shouldn't they be excluded from the denominator of the probability? In the random walk problem, is the number of possible up/right steps really 2^10? If we randomly pick either ‘up’ or ‘right’ ten times, then we will get some paths that take us beyond the boundaries of the grid like 10 consecutive up movements or 10 consecutive right movements. Since these are impossible, shouldn’t they be excluded from the denominator of the probability?

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