On modified $10 \times 10$ chess board Alan and Peter starts moving towards each other with constant speed.Alan can move only two right and upwards. Peter can move only to left and downwards alone lines of chess board.Find number of ways Alan and Peter meet at some point during their trip.
My Try: I assumed they start at diagonally opposite corners.
So if Alan takes $x$ steps horizontally to right and $y$ steps vertically Up , Then to meet Alan ,Peter has to take $10-x$ steps horizontally left and $10-y$ steps Vertically down.
Hence totally they cover $10$ horizontal steps and $10$ vertical steps.
But now how to proceed?