Pascal's Triangle

  • Thread starter kerrwilk
  • Start date
  • #1
14
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Homework Statement



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



Homework Equations





The Attempt at a Solution



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

There are 40 different paths. Is this correct? Thanks for your help.

Note: I only put dots to center the pattern. They have no meaning.
 

Answers and Replies

  • #2
eumyang
Homework Helper
1,347
10
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

You can use the CODE tags to line up letters better, like this:
Code:
   B
  I I
 N N N
O O O O
 M M M
  I I
   A
  L L
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,833
963
It's not clear what you mean by that. You title this "Pascal's triangle" but you appear to have the number of letters in each row coming back to 1 at "A" and than back to 2 at "L".

If you really mean Pascal's triangle so that the number of letters in each row increases so that there are 8 "L"s in the final row, then at each step (at each letter) except the last, you have 2 choices which way to go. Since you are making 7 choices, you have [itex]2^7[/itex] possible paths.
 

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