Number of Pathways

Probability Level 1

How many distinct paths consisting of steps only right or down are possible from P P to Q Q ?

3360 440 100 20

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Tanay Gaurav by tanay gaurav , 24, India

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3 solutions

Tanay Gaurav
Dec 10, 2015

Solution:

Here we see that by travelling through any way, we have to take 3 horizontal and 3 vertical steps. So no of ways of arranging hhhvvv = (6!/3!3!) = 20 ways

8 Helpful 0 Interesting 0 Brilliant 0 Confused

But why did you take factorials?

jaskaran singh sodhi - 5 years, 5 months ago

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By the rule of permutation, number of ways of arranging n items out of which k and x items are similar is given by (n!/k!*x!). Please refer to 'pnc' for further reference.

tanay gaurav - 5 years, 5 months ago

thats right

Tanvir Mitul - 5 years, 4 months ago
Vijay Simha
Jan 14, 2016

What if this problem was modified to : How many distinct paths consisting of steps only right or down are possible from P to Q which are always below the diagonal PQ

In that case Catalan numbers come into play.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

There are ( 6 3 ) = 20 \binom{6}{3} = 20 ways to arrive to Q from P ( just right and down steps)

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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