How many different paths will spell the word BINOMIAL in the following arrangement(moving diagonally downwards to the left or right)?
...B
..I I
.N N N
O O O O
.M M M
..I I
...A
L L
My Answer:
Starting from B using Pascal's Triangle
...B
..1 1
.1 2 1
1 3 3 1
.4 6 4
.10 10
...20
.20 20
Note: the dots are only to center the pattern. They have no meaning. Did I do this correctly? Thanks a lot for your help.
Sorry, whenever I post, the pattern does not come out right. There should be one "I" diagonally down and to the right and one to the left of B. Same pattern with all the other letters. Thanks
Great job on using Pascal's Triangle to solve this problem! Your approach is correct, and you have filled out the triangle correctly for the word BINOMIAL.
However, to determine the number of different paths that spell the word BINOMIAL in the given arrangement, we need to add up the numbers in the diagonal line of Pascal's Triangle corresponding to the length of the word.
In this case, the word BINOMIAL has 8 letters. So, we add up the numbers in the 8th diagonal line, which are: 1 + 6 + 4 + 20 = 31.
Therefore, there are 31 different paths that will spell the word BINOMIAL in the given arrangement by moving diagonally downwards to the left or right.