Page 285 - ABCTE Study Guide_Neat

{ketchup, mustard, mayonnaise, lettuce, onion, pickles, tomatoes}

Once you’ve picked one of the seven toppings and put it on your burger, there are six left to choose from.
Once you’ve picked one of the six remaining toppings, there are five left to choose from - and so on.
There are 5,040 ways to prepare a burger with seven toppings.

What we've been discussing are factorials, which are the product of all integers less than or equal
to n, the number of objects in the set. This is expressed as n! For example, here's what it looks like for a
set of 4:

4! = (4)(3)(2)(1) = 24

Give it a try other examples like 5! or 10! Notice how quickly permutations get enormous. The ability to
capture this information with an exclamation mark after a number is what makes mathematics such a
useful symbolic language and powerful tool as we explore and learn about our world.

Question

There are five people on a bicycle racing team. They always ride in a pace line, with one cyclist behind
another. How many ways are there for the team to ride in a line?

A 5

B 15

C 20

D 120

Answer

Choice D is the correct answer. The fundamental counting principle applies here, so there are 120 ways
for the cyclists to ride in a line.

Simple Events And Compound Events

A simple event consists of one trial of an experiment, like rolling a die once.

A compound event consists of more than one trial, like picking a card from a standard deck, returning it,
and picking another card.

Suppose there are four coins in your pocket: a quarter, a dime, a nickel, and a penny. Suppose you pick
one coin and then pick a second coin. What’s the probability that the second coin is the penny?
It depends.

Two events are independent if the outcome of the first does not affect the outcome of the second. Two
events aredependent if the outcome of the first does affect the outcome of the second.

Question

Which of the following experiments is an example of two dependent events?