IIT JEE , AIEEE Forum - Mathematics , Algebra - oues1) show that 72C36 IS DIVISIBLE BY 73

anki016

72C36 - 1
= 72 * 71* 70 *........*37/1*2*..........*36 - 1
=(73-1)*(73-2)*(73-3)*..........(73-36) - 1 * 2* 3*4 *..............36 /1*2*3..........36

now in expansion of (73-1)*(73-2)............*(73-36) there will be only one term without 73 i.e 1*2*3...............*36
and that will get cancelled................ with next -1*2*3.........*36

so 72c36-1 is divisible by 73.........
that was indeed fabulous question!!!!!!!!!!!

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