So I am really stumped on this problem. I am having a hard time drawing it on here for the tutors but any help would be greatly appreciated. You must start at A, which is in the left hand corner, and end at c which is in the right hand corner. B is located one row down from A and three rows across. The question asks how many different routes start at A, pass through B, and end at C if you can only move down or to the right when starting at A and ending at point C.
I can't tell what you mean by these words:
"B is located one row down from A and three rows across."
What do you mean by "three rows across"?
Is it like this, where B is in between the third and fourth
cells on the top (horizontal) row?
A
[-][-][-]B[X][ ]
[ ][ ][ ] [ ][ ]
[ ][ ][ ] [ ][ ]
[ ][ ][ ] [ ][ ]
[ ][ ][ ] [ ][Y]C
If so then there is only one way to get from A through B
to cell X, and that is Down,Right,Right,Right (abbreviated
DRRR.) Then to get from cell X to cell Y you must make 1
move right and 4 moves down. So your moves from A
to Y can be any of these 5:
DRRRRDDDD, DRRRDRDDD, DRRRDDRDD, DRRRDDDRD, or DRRRDDDDR
There are only 5 ways
Or is it like this, where the B is located between
the 2nd and 3rd cells on the top row?:
A
[ ][ ]B[X][ ][ ]
[ ][ ] [ ][ ][ ]
[ ][ ] [ ][ ][ ]
[ ][ ] [ ][ ][ ]
[ ][ ] [ ][ ][Y]C
If so, there is only one way to get from A to X,
which is DRR.
Then to get fron cell X to cell Y, you must make
2 moves right and 4 moves down.
So it's the same as the number of distinguishable
ways to arrange RRDDDD
6!/(2!4!) = 15. The 15 complete moves from A to C
through B are these, which all start with DRR which
is the only way to go through B to get to cell X.
1. DRRRRDDDD
2. DRRRDRDDD
3. DRRRDDRDD
4. DRRRDDDRD
5. DRRRDDDDR
6. DRRDRRDDD
7. DRRDRDRDD
8. DRRDRDDRD
9. DRRDRDDDR
10. DRRDDRRDD
11. DRRDDRDRD
12. DRRDDRDDR
13. DRRDDDRRD
14. DRRDDDRDR
15. DRRDDDDRR
Edwin