Combinations, Permutations & Probability

Combinations, Permutations & Probability

Multiple Choice

A teacher is selecting 6 students to participate in a project out of a class of 18. Would this be a permutation or combination?

• combination

• permutation

Multiple Choice

A teacher is selecting 6 students to participate in a project out of a class of 18. How many different ways can the teacher select this group of 6?

• 13366080

• 80196480

• 2227680

• 18564

• 73440

Multiple Choice

The starting lineup on a basketball team consists of a point guard, shooting guard, small forward, power forward and center. Assuming everyone on the team is capable of playing at each position, how many different starting lineups can be created from a 12-man roster?

• 3391680

• 132

• 792

• 11880

• 95040

Multiple Choice

You are selecting two sides to go with your meal. There are 9 different sides on the menu. How many different ways can you choose your sides?

• 72

• 36

• 18

• 81

• 512

Multiple Choice

In a track event, 8 runners compete for gold, silver and bronze medals. How many different ways can the medals be distributed?

• 1680

• 40320

• 336

• 56

• 6720

Probability is the measure of how likely an event is to occur.

• Each possible result of a probability experiment or situation is an outcome.

• The sample space is the set of all possible outcomes.

• An event is an outcome or set of outcomes.

Favorable outcomes are outcomes in a specified event.

Examples:

• The probability of drawing a heart from the standard deck of 52 cards. The favorable outcome is drawing a heart.

• The probability of rolling a sum of 12 when rolling a pair of dice. The favorable outcome is rolling a 12.

Equally likely outcomes have the same chance of occurring.

Examples of situations with equally likely outcomes:

• Rolling a number cube (one die) with a sample space of {1, 2, 3, 4, 5, 6}. The probability of rolling a 3 is the same probability of rolling a 4. They both have probability of 1/6.

• Flipping a fair coin with a sample space of {heads, tails}. Landing on heads has the same probability of landing on tails. They both have probability of 1/2.

The sum of all probabilities in the sample space is 1.

Suppose you roll a 6-sided number cube.

• The sample space is {1, 2, 3, 4, 5, 6}.

• The probability of rolling a 1 is 1/6.

• The probability of rolling a 2 is 1/6.

• The probability of rolling each number is 1/6 (equally likely outcomes).

Suppose you roll a 6-sided number cube.

• If you add up all probabilities in this sample space, the result is 1.

• Add the probability of rolling a 1, rolling a 2, ..., rolling a 6.

• 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1

The complement of an event is the set of all outcomes in the sample space that are not in the event.

• The probability of rolling a 4 is 1/6.

• The probability of the complement of rolling a 4 is

   $1-\frac{1}{6}=\frac{5}{6}$  

• The probability of the complement of event A is 1 minus the probability of A.

Multiple Choice

The probability of event A, P(A), equals 2/3 and the probability of event B, P(B), equals 1/8. What is the complement of the probability of event A?

• ~P(A)=2/3

• ~P(A)=1/3

• ~P(A)=1/8

• ~P(A)=7/8

• ~P(A)=1/12

Multiple Choice

Event A=rolling a 2 on a six-sided number cube

Event B=flipping a coin and landing on tails

What is the probability of event B, P(B)?

• 1/2

• 1/4

• 2

• 1

Multiple Choice

Event A=rolling a 2 on a six-sided number cube

Event B=flipping a coin and landing on tails

What is the probability of the complement of event A, ~P(A)?

• 1/6

• 2/3

• 5/6

• 1/2

• 1/3