Question 1114944
I think it would be  20C6 * 14C4 * 10C3 * 7C7 = {{{ highlight( 4655851200 )  }}} ways.
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It seems arbitrary to assign the group of 6 workers first, but this result is independent of which group you assign first.  Even if you group, say, the 7 workers first for their job, the result is the same:

20C7 * 13C6 * 7C4 * 3C3 = {{{ highlight ( 4655851200 ) }}} ways.
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Of course, more complex assignments are possible (assign job 1 to a person from group of 6, assign job 2 to a person from the group of 3, etc.), but the number of possible ways should still be the same.