Combinatorics, probability and statistics Questions

[Numbnut247]

Hey guys, I have a few questions:

1. There are 35 desks in a classroom. In how many ways can the teacher configure a seating plan for a class of 30 students?

I'm not sure if order matters (35P30 or 35C30).

2. Sixteen people attend a meeting. Each person greets everyone with a single handshake. Find the total number of handshakes that are exchanged.

Each person shakes 15 other people's hand but half of them are repeated so is it (15!)/2

3. A manufacturer determines that the volume of juice in a juice box is normally distributed with a minimum of 244mL and a maximum of 256mL. What is the best estimate of the standard deviation? Complete it without the use of a calculator.

I got 250mL as my mean by (244+256)/2. I'm thinking the minimum and maximum should be about 95 percent of the good so the standard deviation is 3?

Thanks

 

[Galileo]

Hey guys, I have a few questions:

1. There are 35 desks in a classroom. In how many ways can the teacher configure a seating plan for a class of 30 students?

I'm not sure if order matters (35P30 or 35C30).

If you take 35C30, you have the number of ways to pick 30 seats out of 35 (the ones that will be occupied). But for every choice of these 30 occupied seats, every permutation of the 30 students will give a different seating plan.

2. Sixteen people attend a meeting. Each person greets everyone with a single handshake. Find the total number of handshakes that are exchanged.

Each person shakes 15 other people's hand but half of them are repeated so is it (15!)/2

Phew, 15!/2 is a big big number! If two handshakes would be exchanged every second you'd still be shaking after 10,000 years.

It's true that each person shakes 15 hands and then you count double, but that doesn't lead to 15! (=15*14*13*...*1)

 

[Numbnut247]

Got it, thanks a lot guys