Joint meeting of the company elects the president, chairman and 10 members
of the Board of Directors from 50 employees. In how many ways can this be done?

We can choose the president any of 50 ways.
We can then choose the chairman in any of the remaining 49 ways.
We can then choose the 10 members of the board of directors as
'48 remaining members, choose 10' or 48C10

That's 50*49*(48C10) = 50*49*6540715896 = 16024753945200 ways.

That's 16 trillion plus billions and billions more!

Edwin