DISCRETE MATH! PLEASE ONLY ANSWER IF YOU CAN ANSWER ALLL, THANK YOU! 10.3.2: Str
ID: 3120387 • Letter: D
Question
DISCRETE MATH! PLEASE ONLY ANSWER IF YOU CAN ANSWER ALLL, THANK YOU!
10.3.2: Strings with no repetitions.
1) How many strings are there over the set {a, b, c} that have length 10 in which no two consecutive characters are the same? For example, the string "abcbcbabcb" would count and the strings "abbbcbabcb" and "aacbcbabcb" would not count.
10.5.4: Counting strings of letters.
2)How many different strings of length 12 containing exactly five a's can be chosen over the following alphabets?
(a)The alphabet {a, b}
(b)The alphabet {a, b, c}
10.5.5: Choosing a chorus.
3) There are 30 boys and 35 girls that try out for a chorus. The choir director will select 10 girls and 10 boys from the children trying out. How many ways are there for the choir director to make his selection?
Explanation / Answer
1) For the first place we can choose any character from a, b and c. For, the second place we can not choose the character which was choosen on the first place, so for the second place we have only two option. Again, in the third place we can choose the character which was choosen on the second place, so for the third place again we have two choices. In the same way, for a string of length 10 with no two consecutive characters repeated, we the total number of strings as
3*2*2*2*2*2*2*2*2*2
=3*(2)^9
=3*512
=1536
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