Question 528682
I'll take shot at it, but you might want to get 
a 2nd opinion
Since the treasurer must be a lady, there are 
60 different ways that office can be filled
Since the Secretary must be a man, there are
40 ways that office can be filled.
There are {{{ 60*40 = 2400 }}} different ways
that the 2 offices can be held
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Once the Treasurer and Secretary offices have
been filled, there are {{{ 59 + 39 = 98 }}}
people left to fill President and Vice-President
There are {{{ 98*97 }}} different ways to fill
these 2 offices ( M or F doesn't matter )
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The 4 offices can then be filled in
{{{ 60*40*98*97 }}} different ways.
( I lost calculator, you can finish )