Thread: (2) Probability Q's

1.) In a club of 10 members...How many ways are there to choose a President, and an Advising Council of 3 members?

2.) A deli offers ham sandwiches, roast beef sandwiches, cheese sandwiches, turkey sandwiches, and salami sandwiches. You are sent in to buy sandwiches for a group of ten people for lunch. How many different ways can you order lunch?

3.) In a club of 10 members...How many ways are there to choose a President, a Vice President, a Secretary, and a Treasurer?

I'm I correct w/ using nCr (n=10,r=4) .... which equals 210 different ways?

Yes, $\displaystyle \frac{10!}{4! \cdot (10-4)!} = 210 $

For Q1, you can choose a president 10 ways, and then for each choice of president, your council will consist of three people from a group of nine.

$\displaystyle 10 \cdot \frac{9!}{3! \cdot (9-3)!} = 840 $

For Q2, I think the answe is (n+k-1)C(k) .

Originally Posted by toop

1.) In a club of 10 members...How many ways are there to choose a President, and an Advising Council of 3 members?

2.) A deli offers ham sandwiches, roast beef sandwiches, cheese sandwiches, turkey sandwiches, and salami sandwiches. You are sent in to buy sandwiches for a group of ten people for lunch. How many different ways can you order lunch?

3.) In a club of 10 members...How many ways are there to choose a President, a Vice President, a Secretary, and a Treasurer?

I'm I correct w/ using nCr (n=10,r=4) .... which equals 210 different ways?

2) You have 5 possible sandwich choices for each of the 10 people, so the number of possibilities is $\displaystyle 5^{10}$.

awkward, I don´t think that is what he meant. I think he meant that you go into the diner and need to buy 10 sandwiches. The order is irrelevant.
That´s the way I interpreted the question.

Originally Posted by Twig

awkward, I don´t think that is what he meant. I think he meant that you go into the diner and need to buy 10 sandwiches. The order is irrelevant.
That´s the way I interpreted the question.

Hi Twig,

That's a good point-- it depends on the interpretation of the question. To me it seems that the question of who gets which sandwich is relevant-- it would matter if it was my sandwich! But either interpretation is plausible.

Awkward

Definetely