A baseball team roster consists of 20 players of which 14...

A baseball team roster consists of 20 players, of which 14 are considered active. Answer the following questions using either the permutation or the combination notation. (a) How many ways are there for a manager to select 14 active players from the roster? (b) How many ways can a manager select a 9-player batting lineup from the active roster for opening day? (a) There are 20 choose 14 ways to select 14 active players from the roster. (Type a whole number.)

Transcript

00:02 All righty, guys.

00:04 Let's go and get started on this one here.

00:06 So it looks like we're talking about a baseball team.

00:10 And our roster consists of 20 players, and we need to get 14 of them active, which means we need to choose working players to become active, which means we're either dealing with a permutation or a combination.

00:22 All right.

00:22 So now let's think about this.

00:24 As a manager of the team, what we have to ask ourselves is the order.

00:27 Does the order in which we pick them matter? okay, so two famous baseball players, maybe mike trout and bryce harper.

00:33 Would it matter if i picked bryce harper first and then put mike, picked mike trout second? well, in this case, no, not really.

00:40 Either way, they end up being active, okay? because right now we're not talking about order in which position they're playing or where they're hitting in the batting order.

00:47 We're just talking about them being active.

00:49 So whether i pick one first, the other second, doesn't really matter.

00:52 Either way, i get active.

00:53 They're active players, which means i'm going to use the choose function or the combination function.

00:58 So in order to calculate that, i'm going to get my choose function.

01:03 So desmos .com slash scientific.

01:05 This is an absolutely free calculator you can find online.

01:08 I 100 % recommend it.

01:09 And so the choose function is as follows.

01:12 That is ncr, and you'll find them right there.

01:15 So desmos .com scientific, click on the func...