Give a formula to get no. of ways in which a rook can travel from SOUTH W corner of chessboard to NORTH EAST?

Question

the chessboard is of P x Q dimensions.rook travels only vertically or horizontally.only one move at a time is allowed and the direction can be in the north or east side.i want all the total possible no. of ways.

Answer 1

Ionly do the cases that P>1 and Q>1

the number of moves you make to the North are P-1
the number of moves you make to the East are Q-1
the order of the moves doesnt matter You can do first all the North's then the East, or first some Noths then some easts.

So in total you do P+Q-2 moves , imagine a string of P+Q-2 signs, put P-1 plus signs and Q -1minus signs in it, this can be done in (P+Q-2) C (P-1) or which is the same (P+Q-2) C (Q-1)

P =1 then there are Q-1 moves
Q = 1 then there are P-1 moves

Answer 2

If the rook is not allowed to go the a square more than once, then at any point, the rook has 2 options to go to north or east

so, ur answer is 16C8 ways

Not 14C7 as said in the previous answer. That would be so, if the chess grid in 7x7

Answer 3

The total possible number of ways is 14C7, or 3432. To get from corner to corner moving one space at a time, you have to take 7 moves north and 7 moves east. You're counting 14 moves (in total), taken 7 (north moves) at a time.

Answer 4

You can only make p-1 moves to the east and q-1 north. as you must make these moves and the order that you take these moves determine your path, you have (p-1)(q-1)

Answer 5

Well, if the rook is allowed to visit the same space twice, it would be infinite.

If not, I have no idea.

Answer 6

It could be any way. Up, down, any direction. It's infinite.

Answer 7

just take the freeway LOL