Farrooh F. answered • 01/12/17

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101!/(99!*2!) = 101*100/1*2 = 101*50 =5050.

Alternatively, you can solve it this way. Line 1 crosses all 100. Line 2 does the same, but we already counted 1, so it does 99. And line 3 does 98, line 4 does 97, etc. Thus the sum of 1 to 100 is needed which is easily obtained by doing arithmetic progression: 5050.

Mark M.

01/12/17