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  • The number of (staircase) paths in the plane from <img alt="\mathrm{(0,0) \, to \, (7,5)}" sr

The number of (staircase) paths in the \mathrm{x y-} plane from \mathrm{(0,0) \, to \, (7,5)} where each such path is made up of individual steps going one unit upward \mathrm{(U)} or one unit to the right \mathrm{(R)}. One such path is shown in Fig. 6.3

Option: 1

\mathrm{{ }^{12} C_5}


Option: 2

12 !


Option: 3

5 ! 7 !


Option: 4

\mathrm{{ }^{12} P_5}


Answers (1)

best_answer

The number of paths

=  the number of ways of arranging \mathrm{5 \, U^{\prime} S\, and \, 7 \, \, R^{\prime} \mathrm{s}}.

\mathrm{=\frac{12 !}{5 ! 7 !}={ }^{12} C_{5}}

Posted by

Ritika Kankaria

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