Question

Find the number of all combinations of 8 objects a, b, c, d, e, f, g, and h taken 7 at a time.

Answer 1

Are you familiar with the nCr notation?

Answer 2

noooo we are supposed to use permutations i believe

Answer 3

No, this is not a permutation problem.

Answer 4

This is a combination problem.

Answer 5

ohhhhh yes you ar correct. can you help me with it?

Answer 6

Are you familiar with nCr and what it means?

Answer 7

noo i am not

Answer 8

Ok. Well it is a notation to solve this exact problem.

Answer 9

do you know the answer?

Answer 10

nCr is an expression which tells you how many different combinations of r different things you can make from a pool of n things.

Answer 11

Does that make sense?

Answer 12

yes

Answer 13

ok, so in this case how big is our pool?

Answer 14

8?

Answer 15

Correct. And how many things will we be taking from the pool to make our combinations?

Answer 16

7?

Answer 17

Correct.
So the answer to this problem is 8C7

Answer 18

But that doesn't help much cause they want a real number.

Answer 19

So now, let me give you the formula for nCr, and you can use it to find 8C7

Answer 20

okay! great!

Answer 21

\[nCr \equiv \frac{n!}{r!(n-r)!} \]

Answer 22

So can you use that to figure out what 8C7 is?

Answer 23

282240?

Answer 24

is this the correct answer?

Answer 25

\[\frac{8!}{7!(8-7)!} = \frac{8!}{7!1!} = \frac{8!}{7!}\]

With me so far?

Answer 26

ohhhhh yess!!!! i put it all together! now i see!

Answer 27

So what is the answer?

Answer 28

8?

Answer 29

Correct.

Answer 30

you are so helpful!!!

Answer 31

i have another question! can you help me?

Answer 32

How many ways are there to seat 4 people in a 9-passenger automobile? Assume that some times there will be no one in the driver's seat.