Question

Help! :/
Nineteen students play on a baseball team. How many ways can the batting order of 10 players be arranged?

Answer 1

You want to find how many permutations of 10 there are from 19 people.
So you calculate:
19P10
Do you know how to use this button on your calculator?

Answer 2

I do not.

Answer 3

If not, it's exactly:
\[\frac{19!}{9!}\]

Answer 4

How did you get that?

Answer 5

The formula for nPr is:
\[\frac{n!}{(n-r)!}\]
nPr basically means "how many k permutations of n are there?"
Does this make more sense? Also do you understand what I mean by factorial (!)?

Answer 6

Yes and no

Answer 7

Oh, no for the factorial? Factorial just means multiply that number by every positive number before it. So 9! means 9x8x7x6x5x4x3x2x1.
Is this a homework question? If so I'm surprised that they'd give you this before explaining about factorials :P

Answer 8

Yes I do online, this is just a practice but i just don't understand it, but that did help alot. So i get the 9x8x7x6x5x4x3x2x1 but how did you get 9?

Answer 9

In fact I think I may have chosen the wrong one. It's nCr not nPr.
The formula for nCr is:
\[\frac{n!}{r!(n-r)!}\]
Which is a lot smaller and looks like a more sensible answer. So for this question it'd be:
\[\frac{19!}{10!\times 9!}\]
You can work this out on a calculator or on wolfwram, it comes out as 92,378.
Sorry about that :)

Answer 10

nCr means "how many ways are there of choosing r from n".