How Many Ways Are There To Select 7 Countries In The United Nations To Serve On A Council If 2 Is Selected From A Block Of 52, 2 Are Selected From A Block Of 65 And 3 Are Selected From The Remaining 72 Countries?

There are (52)(51)/2 = 1326 ways to select 2 from 52.
There are (65)(64)/2 = 2080 ways to select 2 from 65.
There are (72)(71)(70)/((3)(2)) = 59,640 ways to select 3 from 72.
The council could be constituted (1326)(2080)(59640) = 164,491,891,200 different ways.

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If the delegates were not chosen by block, there would be about 10 times that many ways to constitute the council.