How Many Ways?

Number Theory Level 1

There are 4 letters in a sequence: A, B, C, and D.

How many ways can we rearrange these letters?


The answer is 24.

Fred Fan by fred fan , 21, Canada

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3 solutions

Since no letters are alike, we can arrange the 4 4 letters in 4 ! 4! or 4 ( 3 ) ( 2 ) ( 1 ) = 24 4(3)(2)(1)=24 ways.

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Angela Fajardo
Apr 10, 2015

It can be arranged in 4! ways or 4 x 3 x 2 x 1 = 24

Or you can also list it

ABCD ABDC ACBD ACDB ADBC ADCB

BACD BADC BCAD BCDA BDAC BDCA

CABD CADB CBAD CBDA CDAB CDBA

DABC DACB DBAC DBCA DCAB DCBA

But it's shorter if you 4! = 4 x 3 x 2 x 1 = 24

So, the number of ways it can be arranged is 24

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4 ! = 4 × 3 × 2 × 1 = 24 4! = 4 \times 3 \times 2 \times 1 = 24 . Please check your solution.

Simon Frohlich - 5 years, 8 months ago

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sorry for the typo...

Angela Fajardo - 5 years, 8 months ago

There is a typo error in the first line of your solution, it was addressed by Simon Frohlich 1 1 year and 6 6 months ago from now (today is April 11, 2017). Until now it was not edited.

A Former Brilliant Member - 4 years, 2 months ago

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Thanks for that

Angela Fajardo - 4 years, 1 month ago
Krishna Shankar
Apr 10, 2015

The 4 letters in a sequence a b c & d can be arranged in 4! ways =24

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