The total number of possible ways in which a | vedclass

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Question

(B) To go from $A(0,0)$ to $B(3,3)$ on a $3 	imes 3$ grid,a person must take a total of $6$ steps: $3$ steps to the right $(H)$ and $3$ steps upward

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(B) To go from $A(0,0)$ to $B(3,3)$ on a $3 	imes 3$ grid,a person must take a total of $6$ steps: $3$ steps to the right $(H)$ and $3$ steps upward $(V)$.The total number of ways to arrange these $6$ steps is given by the number of permutations of $6$ items where $3$ are of one type and $3$ are of another type.This is calculated using the formula for combinations: $\binom{n+m}{n} = \frac{(n+m)!}{n!m!}$,where $n=3$ and $m=3$.Total ways = $\binom{3+3}{3} = \binom{6}{3} = \frac{6 	imes 5 	imes 4}{3 	imes 2 	imes 1} = 20$.Therefore,there are $20$ possible ways.

The total number of possible ways in which a person can go from point $A(0,0)$ to point $B(3,3)$ if they can travel only to the right or upward along the grid lines is equal to:

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