Question 891977: consider strings of length 10 which contain only letters from the set{A,E,I,O,U} and digits from {1,3,5,7,9}suppose repetition of letters is not allowed.
a) how many different strings are there?
b) How many different strings are there if the letters,i.e A,E,I,O,U and the digits,i.e 1,3,5,7,9 must alternate?
c) How many different strings are there if all five letters must be adjacent in each string?
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website! consider strings of length 10 which contain only letters from the set{A,E,I,O,U} and digits from {1,3,5,7,9}suppose repetition of letters is not allowed.
a) how many different strings are there?
P(10,10) = 10! = 3628800
b) How many different strings are there if the letters,i.e A,E,I,O,U and the digits,i.e 1,3,5,7,9 must alternate?
They can go either
LDLDLDLDLD or DLDLDLDLDL, where D stands for a digit and L for a letter.
There are P(5,5) = 5! = 120 ways the letters can be arranged times
P(5,5) = 5! = 120 ways the digits can be arranged. Then we multiply by
2 because we can either start with a letter or a digit.
Answer: 5!*5!*2 = 120*120*2 = 28800.
c) How many different strings are there if all five letters must be adjacent in each string?
Think of (AEIOU) as a single thing. Then there are these 6 things
to rearrange:
1,3,5,7,9,(AEIOU)
which is P(6,6) = 6! = 720. But we must multiply this by P(5,5) = 5! since the
letters (AEIOU) can be rearranged in 5! ways.
Answer 6!*5! = 720*120 = 86400
Edwin
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