1. How many different license plates are available if the license plate pattern
ID: 2963908 • Letter: 1
Question
1. How many different license plates are available if the license plate pattern consists of 4 letters followed by 3 digits? Assume all letters are uppercase and the digits are 0,1,2,...,9.
Duplicates are okay.
D. 264 * 103
2. How many bit strings (strings of 0's and 1's) are there of length 7 that have more 0's than 1's?
A. 26 * 25 * 24 * 23 * 10 * 9 * 8 B. 26*26*26*26 * 10 * 9 * 8 C. C(26,4) * C(10,3)D. 264 * 103
2. How many bit strings (strings of 0's and 1's) are there of length 7 that have more 0's than 1's?
A. 24 + 25 + 26 + 27 B. C(7,4) + C(7,5) + C(7,6) + C(7,7) C. 2*2*2*1*1*1*1 D. C(7,4) * C(7,5) * C(7,6) * C(7,7)Explanation / Answer
1. D. there are 26 choices for each of the letters and 10 choices for each of the digits.
2. B. there are C(7,4) ways to make a string with 4 0's and 3 1's, C(7,5) ways to make a string with 5 0's and 2 1's, C(7,6) ways to make a string with 6 0's and 1 1's, C(7,7) ways to make a string with 7 0's and 0 1's. Add these up to get the total.
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