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The total number of ways one can reach $(5,5)$ from $(0,0)$ is $^{10}C_5$ as per a tutorial I am following. I know there are $5$ rights and $5$ ups. So there are 10 steps. But why it is choose $5.$

true blue anil
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Splendid Digital Solutions
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    A path from $(0,0)$ to $(5,5)$ will look something like $RRUURUURRU$ i.e. it will have five $R'$s and five $U'$s. So once we choose five spots for one type then the other five spots automatically will have to be of the other type. – Anurag A Jul 31 '21 at 06:01
  • This way to visualize helped me understand. – Splendid Digital Solutions Jul 31 '21 at 06:19

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There are 10 steps, and you choose 5 of them to be rights.

user951252
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