Joe wants to find all the four-letter words that begin and end with the same letter. How many combinations of letters must he examine? A word is any sequence of letters, such as MTHM, and does not have to be English. (You can use a calculator for this problem.)

Guest Apr 6, 2018

#2**+1 **

the answer is 26^{3}, because the first letter and the last letter are the same.

This means that picking a four letter word that follows this rule is just like picking any 3 letter word (pick a 3 letter word, and then add a "copy" of the first letter as a fourth letter)

for example- \(Dye\Rightarrow Dyed\)

so there's a total of 26^{3} =17,576 combinations- 26 options for the first letter, 26 options for the second letter, and 26 options for the third letter.

Guest Apr 6, 2018

edited by
Guest
Apr 6, 2018

#1**+1 **

He would have to look a 26^{4} combinations.

This is because:

2 letter words =

AA to ZZ

AA to AZ is 26 combinations, then you repeat with BA to BZ, CA to CZ etc.

As you repeat this 26 combo thingamajig 26 times,

This means that there are 26^{2} combinations for two letter words.

3 letter words =

AAA to ZZZ

AAA to AAZ is 26 combinations, AAA to AAZ is 26 combinations.

then you repeat with ABA to ABZ, etc.

This means that there are 26^{3} combinations for three letter words.

Therefore..

4 letter words =

AAAA to ZZZZ

AAAA to AAAZ is 26 combinations, then you repeat with AABA to AABZ, AACA to AACZ etc.

This means that there are 26^{4} combinations for four letter words.

Not sure about the answer though...

thejamesmachine
Apr 6, 2018

#2**+1 **

Best Answer

the answer is 26^{3}, because the first letter and the last letter are the same.

This means that picking a four letter word that follows this rule is just like picking any 3 letter word (pick a 3 letter word, and then add a "copy" of the first letter as a fourth letter)

for example- \(Dye\Rightarrow Dyed\)

so there's a total of 26^{3} =17,576 combinations- 26 options for the first letter, 26 options for the second letter, and 26 options for the third letter.

Guest Apr 6, 2018

edited by
Guest
Apr 6, 2018