1.2 Permutations

The Game: draw 3 cards for your stack. Take the face value of the first, double the face value of the second, triple the face value of the third. Opponent repeats the process, highest score wins.

What’s the highest possible score?

What’s the lowest possible score?

How many different outcomes are there?

What if the game required you to draw 8 cards, how many outcomes are there?

Factorials provide a method to reduce this notation to something simple.

Factorial Notation – multiply by every proceeding whole number down to 1

Ex 1 Calculate Ex 2 Evaluate

(a) 2! (b) 4! (c) 8! (a) (b)

Ex 3 A band has prepared 5 songs for an upcoming gig. How many different sets could they perform?

Ex 4 In how many ways could ten questions on a test be arranged, if the easiest and hardest question are:

(a) side by side?

(b) not side by side?

Permutation – an arrangement of items in a definite order.

Ex 5 There are eight members on student’s council giving speeches at the next assembly. How many permutations of speeches are there?

Ex 6 How many permutations are there of n objects?

Ex 7 How many permutations are there of n objects taken r at a time?

Permutation Notation:

Ex 8 In solitaire, there are 21 cards hidden. How many different ways could those 21 cards be dealt out?

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