Unit 7 Probability Notes

Use the Multiplication Rule for Counting to determine the number of permutations.

Compute expressions containing factorials.

Compute permutations.

Apply permutations to solve problems.

0

1

n

Infinity

56

720

40,320

24

n!/(n-r)!

n!/r!

(n+r)!/n!

n!/(n+r)!

Order does not matter in combinations.

Order matters in combinations.

Combinations are the same as permutations.

Combinations cannot be used for lists.

n!/(n-r)!

n!/(r!(n-r)!)

r!/(n!(n-r)!)

n!/(r!r!)

{H, T}

{0, 1, 2, ..., 10}

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

{Heads, Tails}

The experiment must have only two stages and the outcomes of each stage must have no effect on the outcomes of the other.

The experiment must have more than two stages and the outcomes of each stage must affect the outcomes of the other.

The experiment must have only one stage and the outcomes must be random.

The experiment must have dependent stages and outcomes must be identical.

The outcome of one stage affects the other

The outcome of one stage does not affect the other

Both stages must have the same outcome

Both stages must have different outcomes

Probability is always greater than 1

Probability can be negative

Probability is always between 0 and 1

Probability is always equal to 0

P(E) = n(S)/n(E)

P(E) = n(E)/n(S)

P(E) = n(E) + n(S)

P(E) = n(E) - n(S)

1/13

1/26

1/52

1/10