Question

a 50 member club wants to choose a president, 2 vice-president 3 secretaries and 2 treasures derive the number of ways

Answer 1

there are \(50\) ways to choose the president
after that there are 49 people from which to choose the two vice presidents, there are
\[\binom{49}{2}=\frac{49\times 48}{2}=49\times 24=1176\] ways to do that

then there are 47 people out of which you have to choose 3 secretaries
there are \(\binom{47}{3}\) ways to do that
etc
once you get done, multiply all these choices together

Answer 2

@satellite73 for choosing the president it will be C(50,1) right ?