In a committee, there is only one chairman, 2 secretaries, and 3 members. If there are only 6 people, how many ways are there to assign them these positions? If there are 2 candidates for chairman, 4 candidates for secretary positions, and 5 candidates for the members position, how many ways are there to get such a committee?

thank you

i did 6 pick 1 x 6 pick 2 x 6 pick 3= 3600

does anyone know if this is correct!?
any help is greatly appreciated

Hello, rsalort!

In a committee, there is only one Chairman, 2 Secretaries, and 3 Members.
If there are only 6 people, how many ways are there to assign them these positions?

From the six people, choose one to be Chairman: .$\displaystyle {6\choose1} = 6$ choices.

From the remaining five people, choose two to be Secretaries: .$\displaystyle {5\choose2} = 10$ choices.

From the remaining three people. choose three to be Members: .$\displaystyle {3\choose3} = 1$ choice.

Therefore, there are: .$\displaystyle 6\cdot10\cdot1 \:=\:60$ ways to form the committee.

If there are 2 candidates for Chairman, 4 candidates for Secretary, and 5 candidates
for the Members positions, how many ways are there to get such a committee?

From the 2 Chairman candidates, choose one Chairman: .$\displaystyle {2\choose1} = 2$ choices.

From the 4 Secretary candidates, choose two Secretaries: .$\displaystyle {4\choose2} = 6$ choices.

From the 5 Member candidates, choose 3 Members: .$\displaystyle {5\choose3} = 10$ choices.

Therefore, there are: .$\displaystyle 2\cdot6\cdot10 \:=\:120$ ways to form the committee.

thank you soroban, i really appreciate it

for the 2nd part of the question, are there 11 people or still only 6?