Combinatorics Flashcards

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1
Q

What does 10! means

A

It’s the number of arrangements of 10 elements IN DIFFERENT ORDERS
(order matters)

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2
Q

What does 10C5 means

A

It’s the number of groups of 5 that can be created from 10 elements, if order doesn’t matter
(109876) / 5!

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3
Q

What is 10* 9* 8* 7* 6

A

It’s the number of groups of 5 elements that can be created from 10 elements IN DIFFERENT ORDERS
(order matters)

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4
Q

What is a * b* c in combinatorics?

A

The number of groups that can be created from sets A, B and C, if ORDER MATTERS

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5
Q

What is a * b* c / 3! in combinatorics?

A

The number of groups that can be created from sets A, B and C, if ORDER DOESN’T Matter (eliminated repetition)

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6
Q

What to do on a “at least one” combinatorics question?

A

1) draw the scheme
2) understand how you can create the group
3) calcualte the complementary groups (the ones you don’t want)
4) calculate total - complement

APPROACH FROM COMPLEMENTARY GROUPS

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7
Q

What are the options of ordering in combinatorics?

A

Order matters: A,B <> B, A
Order doesn’t amtter: A,B = B,A

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7
Q

How to remove repetitions in combinatorics?

A

If order doesn’t matter, you remove repetition by dividing by the number of repeated groups

In a group of 3, there are 3! possible orders

5C3, you could have 543 groups, but then 3! would be same elements in different orders

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7
Q

How to deal with constraints?

A

Tie the elements together
If on a group of 5 A must not be in corners and be near B, then

3 * 2 * 3 * 2 * 1

If on a group of 5 A must be near B, then

3 * 2 * 3 * 2 * 1
+
2 * 1 * 3 * 2 * 1

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7
Q

If you have 5 books A and 5 books B, how many groups of 3 can you create with at least one A and one B?

A

10C3 - 5C3 - 5C3

total - groups with only A - groups with only B = groups with at least one of each

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