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# HELP MEEEEE

-5
198
5
+25

How many 4-letter words with at least one consonant can be constructed from the letters A,B ,C ,D , and E ? (Note that b,c d, and  are consonants, any word is valid, not just English language words, and letters may be used more than once.)

HALP

May 3, 2019
edited by ProffesorNobody  May 3, 2019

#1
+106539
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4 letter words with 4 consonants  =  Any of 3 consonants can occupy all 4 positions  = (3)^4  = 81 words

4 letter words with 3 consonants  =   Any of  the 3 consonants can be chosen for any 3  of 4 positions and we have 2 choices for the final position of the vowel....so (3)^3 * 4C3 * 2  =  216 words

4 letter words with 2 consonants  =  Any of the 3 consonants can be chosen for 2 of the 4 positions  and we have  2^2 ways to choose the vowels for the other 2 postions   =    (3)^2 * 4C2 * 2^2  =  216 words

4 letter words with 1 consonant =  And of the 3 consonants can be chosen for 1 of the four positions  and we have (2)^3  ways to choose the vowels for the other 3 positions  =  (3)  * 4C1 * 2^3  = 96 words

So....

81 +  216(2) +96  =  609 words

Another way to see this is that we have  (5)^4  =  625  possible words

And  the number of words that contain no consonants  = (2)^4  = 16

So...the number of words with at least one consonant  =  625 - 16  = 609 words

May 3, 2019
#2
-1

The dictionary defines WORD as "a single distinct meaningful element of speech or writing, used with others (or sometimes alone) to form a sentence and typically shown with a space on either side when written or printed."

By this definitioin, something like BCBD is not a word.

The question should be "How many 4-letter words character strings ... can be constructed..."

in my humble opinion

May 3, 2019
#3
+2547
+2

Yes, but the question noted "any word is valid, not just English language words, and letters may be used more than once" so it had the meaning of "character string"

Most people won't recognize what a character string is so they worded the problem like that.

CalculatorUser  May 3, 2019
#4
+25
-5

yep thx guys

ProffesorNobody  May 3, 2019
#5
-1

Most people won't recognize what a character string is..."

Okay, that makes sense, as long as I have the privilege of redefining words, too.  Thanks.

Some people actually are that dumb, huh?

Guest May 3, 2019