In a chess variant, a "lord" can move one space at a time, either upward, or to the right, or diagonally up and to the right. how many ways are there for a lord to move from the bottom left to top right corner of the 8 by 8 chessboard?

There are 48639 ways for a lord to move from the bottom left to top right corner of the 8 by 8 chessboardFurther explanationThe probability of an event is defined as the possibility of an event occurring against sample space.[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]Permutation ( Arrangement )Permutation is the number of ways to arrange objects.[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]Combination ( Selection )Combination is the number of ways to select objects.[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]Let us tackle the problem.This problem is similar to Pascal Triangle.The Lord can move to the right or up in one way only.We can put "1" in each box on the bottom and left to represent 1 possible movement.To get the possibility of movement to another box, we will add the possibility of movement to the left, right, and diagonal squares as shown in Figure 1.This process is repeated for the next box as shown in Figure 2.Finally, after this process is repeated until the top right box, we get the results as shown in Figure 3.There are 48639 ways for a lord to move from the bottom left to top right corner of the 8 by 8 chessboard.Learn moreDifferent Birthdays : or Independent Events : exclusive : detailsGrade: High SchoolSubject: MathematicsChapter: ProbabilityKeywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation