Textbook Question
Evaluate the expression. *permutation notation* the number of permutations 9 things taken 5 at a time (sub 9)P(sub 5)
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10. Combinatorics & Probability
Combinatorics
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How many options are there for license plates with any three letters (A-Z) followed by any 3 numbers (0-9)?
A
260
B
2340
C
11,232,000
D
17,576,000
Verified step by step guidance1
First, determine the number of options for the letters. Since there are 26 letters in the alphabet and the license plate requires three letters, calculate the number of combinations by multiplying 26 by itself three times: 26 * 26 * 26.
Next, determine the number of options for the numbers. Since there are 10 digits (0-9) and the license plate requires three numbers, calculate the number of combinations by multiplying 10 by itself three times: 10 * 10 * 10.
Now, combine the two results. Since the letters and numbers are independent of each other, multiply the number of letter combinations by the number of number combinations to find the total number of possible license plates.
The formula for the total number of license plates is: (number of letter combinations) * (number of number combinations).
Finally, calculate the result using the formula: (26 * 26 * 26) * (10 * 10 * 10). This will give you the total number of possible license plates.
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