Help to solve question on Permutations and Combinations?

Ten lines are drawn parallel to the x-axis and nine lines parallel to the y-axis. Total number of rectangles (of all sizes) formed by these lines (excluding the axes) is given by

N = Sigma(10 -- 1)*Sigma(9 -- 1) = (9*10/2)*(8*9/2) = 1620 ANSWER.

| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

| x | x | x. | x | x | x. | x | x |

---------------- ----------------- x-axis

from your description, i believe that any rectangles using either of the axes are not to be counted, so available lines are 9 parallel to the x-axis & 8 parallel to the y-axis

# of rectangles 9c2 *8c2 = 36*28 = 1008 <-------

if you say there are 10 & 9 parallel *apart* from the axes,

then 10c2 *9c2 = 1620