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# I got different answers...ah. how many paths are there to spell this word? watch

1. rule: start from the top, and you can only move diagonally to the row below.

B
I I
N N N
O O O O
M M M
I I
A
L L

Is there a mathematical way to do this? Or do we just count? I've tried counting and I got 24 and then 26 the second time And I have to do another question like this too.
2. Is that the correct shape for the letters? If not, use [code][/code] tags.
3. could you space the letters a little better please.
4. I'm not 100% sure, but I believe it is this:

1 * 2 * 3 * 4 * 3 * 2 * 1 * 2 = 288
5. (Original post by mahaneap)
I'm not 100% sure, but I believe it is this:

1 * 2 * 3 * 4 * 3 * 2 * 1 * 2 = 288
You can only chose letters going diagonally...

I think the best way of doing this is just to be systematic with how you list out the number of ways of getting BINOMIAL. Maybe give each letter a subscript (from 1-4) and keep in mind that the subscripts of adjacent letters can only differ by 1...
6. There's a very easy, standard way of doing problems like this. Basically do the same as you would calculating Pascal's triangle to get something like:

Code:
```1
1    1
1   2   1
1   3    3  1
4   6   4
10  10
20```
(the correct diagram for this problem would be a bit bigger, but the principle is the same).
7. That's...ingenious!

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