Question 888585: How many 5 letter code words can be formed using a 27 letter alphabet?
A-repetitions allowed
B-no repetitions allowed
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if repetitions are allowed, then 27^5 = 14348907
if repetitions are not allowed, then 27P5 = 27! / 22! = 9687600
how's this work?
in order to see, try 2 letter code words from 3 letter alphabet of abc.
with repetition = 3^2 = 9
without repetition = 3P2 = 3! / 1! = 6
with repetition, the codes would be:
aa
ab
ac
ba
bb
ac
ca
cb
cc
total of 9.
without repetition, the codes would be:
ab
ac
ba
bc
ca
cb
the same formulas apply to the bigger problem.
the formula for permutation is nPx = n! / (n-x)!
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