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# AMC 10A 2021 I Problem 20 | Enumeration

Try this beautiful Problem based on Enumeration appeared in AMC 10A 2021, Problem 20.

## AMC 10A 2021 I Problem 20

In how many ways can the sequence , , , , be rearranged so that no three consecutive terms are increasing and no three consecutive terms are decreasing?

• 10
• 18
• 24
• 32
• 44

Permutation

Enumeration

Combinatorics

## Suggested Book | Source | Answer

An Excursion in Mathematics

AMC 10A 2021 Problem 20

32

## Try with Hints

We have 5 numbers with us.

So, how many permutations we can have with those numbers?

So, numbers can be made out of those numbers.

Now we have to remember that we are restricted with the following condition -

no three consecutive terms are increasing and no three consecutive terms are decreasing.

Now make a list of the numbers which are satisfying the condition given among all numbers we can have.

Now the list should be -

, , , , , , , , , , ,
, , , , , , , , , , , ,
, , , , , , , .

Count how many permutations are there?

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Try this beautiful Problem based on Enumeration appeared in AMC 10A 2021, Problem 20.

## AMC 10A 2021 I Problem 20

In how many ways can the sequence , , , , be rearranged so that no three consecutive terms are increasing and no three consecutive terms are decreasing?

• 10
• 18
• 24
• 32
• 44

Permutation

Enumeration

Combinatorics

## Suggested Book | Source | Answer

An Excursion in Mathematics

AMC 10A 2021 Problem 20

32

## Try with Hints

We have 5 numbers with us.

So, how many permutations we can have with those numbers?

So, numbers can be made out of those numbers.

Now we have to remember that we are restricted with the following condition -

no three consecutive terms are increasing and no three consecutive terms are decreasing.

Now make a list of the numbers which are satisfying the condition given among all numbers we can have.

Now the list should be -

, , , , , , , , , , ,
, , , , , , , , , , , ,
, , , , , , , .

Count how many permutations are there?

## Subscribe to Cheenta at Youtube

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