Permutations / Arrangements (Leaving Cert Mathematics): Flashcards

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Permutations/Arrangements
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What is a permutation?

Arrangement of objects in a specific order

Key characteristic of permutations

Order of selection matters

What does n!n! (factorial) mean?

Product of all positive integers up to nn

n!n! expanded form

n×(n−1)×(n−2)×…×1n \times (n-1) \times (n-2) \times \ldots \times 1

Formula: Arranging nn distinct objects

n!n!

Formula: P(n,r)P(n,r)

n!(n−r)!\frac{n!}{(n-r)!}

Formula: Permutations with repetition

n!p1!×p2!×…×pk!\frac{n!}{p_1! \times p_2! \times \ldots \times p_k!}

Calculate: 4!4!

2424

Calculate: P(5,3)P(5,3)

6060

Arrangements of letters AAB?

33

Effect of identical objects in permutations

Reduces total permutations

Where permutations are essential

Counting problems and probability

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