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

Question

The number of (staircase) paths in the x y-plane from (0,0) to (7,5) where each such path is made up of individual steps going one unit upward (U) or one unit to the right (R). One such path is shown in figure (A)  12 C5 (B) 12 ! (C) 5 ! 7 ! (D)  12 P5

Tardigrade Admin · Accepted Answer

The number of paths = text the number of ways of arranging 5 U prime S text and 7 R prime text s. =(12 !/5 ! 7 !)= 12 C5

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

$^{12} C_{5}$

12 !

$5! 7!$

$^{12} P_{5}$

The number of paths
$= the number of ways of arranging 5 U^{'} S and 7 R^{'} s.$
$= \frac{12 !}{5 ! 7 !} =^{12} C_{5}$

Q. The number of (staircase) paths in the xy-plane from (0,0) to (7,5) where each such path is made up of individual steps going one unit upward (U) or one unit to the right (R). One such path is shown in figure

12C5​

12 !

5!7!

12P5​

The number of paths = the number of ways of arranging 5U′S and 7R′ s. =5!7!12!​=12C5​

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

$^{12} C_{5}$

$5! 7!$

$^{12} P_{5}$

The number of paths
$= the number of ways of arranging 5 U^{'} S and 7 R^{'} s.$
$= \frac{12 !}{5 ! 7 !} =^{12} C_{5}$