DISCRETE MATH! PLEASE ONLY ANSWER IF YOU CAN ANSWER ALLL OF THEM 10.5.4: Countin
ID: 3120414 • Letter: D
Question
DISCRETE MATH! PLEASE ONLY ANSWER IF YOU CAN ANSWER ALLL OF THEM
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?
4) (6 points) License plate numbers in a certain state consists of seven characters. The first character is a non-zero digit (1 through 9). The next four characters are capital letters (A through Z) and the last two characters are non-zero digits. Therefore, a license plate number in this state can be any string of the form:
Digit-Letter-Letter-Letter-Letter-Digit-Digit
(a) How many different license plate numbers are possible?
(b) How many license plate numbers are possible if no digit appears more than once?
(c) How many license plate numbers are possible if no digit or letter appears more than once?
Explanation / Answer
3) 10 girls and 10 boys can be selected in
30C10 * 35C10 ways = 30045015 * 183579396 ways
4) a) Total plates available = 9 * 26 *26 *26 * 26 * 9 * 9 = 333135504
b) If no digits appear more than once
Total plates available = 9 * 26 *26 *26 * 26 *8 * 7 = 230315904
c) If no digits nd letters appear more than once
Total plates available = 9 * 26 *25 *24 * 23 *8 * 7 = 180835200
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