Using the letters in the word "Chipmunk", how many four-letter "words" (meaning ordered collections of letters)?

There are 6 different consonants and 2 different vowels

As letters can be repeated we must do this in stages

Firstly 3 identical consonants and one vowel

There are 6 ways to select the consonents (CCC, HHH, PPP, MMM, NNN, KKK) and 2 ways to select the vowel (I or U)

Therefore there are 6 * 2 = 12 ways to select the letters

However, you haven't finished there because for each selection there are 4 different arrangements.(calculated as 4! / (3! * 1!) = 4

eg HHHU could be arranged UHHH, HUHH, HHUH or HHHU

Therefore there are 12 * 4 = 48 ways to get a treble and a vowel

Next a double, a different consonant and a vowel

There are 6 ways to get the double (CC, HH, PP, MM, NN, KK), and 5 ways to get the other consonant (it can't be the same as the doubleton).Then 2 ways to select the vowel.

Therefore there are 6 * 5 * 2 = 60 ways to select the letters

Then there are 4! / (2! * 1! * 1!) = 12 ways to arrange them

eg

CCHU, CCUH, CHCU, CUCH, CHUC, CUHC

HCCU, UCCH, HCUC, HCCU, HUCC, UHCC

Therefore there are 60 * 12 = 720 ways to arrange a doubleton, single consonant and vowel

Finally 3 different and 1 vowel

There are 6C3 ways to select the consonants and 2C1 ways to get the vowels

Therefore there are 6C3 * 2C1 ways to select the letters

6C3 = 6! / (3! * 3!) = 720 / 36 = 20 ways

2C1 = 2

Therefore there are 40 ways to select the letters

Once selected any 4 letters can be arranged in 4! ways =4*3*2*1 = 24

Therefore there are 40 * 24 = 960 ways that you can get any 4 different letters where one is a vowel

Finally ADD the three stages together

48 + 720 + 960 = 1728

Answer = 1728

2 words. Chip and munk (both 4 letter words