Beginning with cars made in 1981, all vehicles must contain a 17-digit Vehicle Identification Number (VIN). The first 3 positions must be letters or numbers, position 4 and 5 must be letters, positions 6 and 7 must be numbers, position 8 can be a letter or a number, position 9 is a number, position 10 is a letter or a number, and positions 11 through 17 must be numbers. All numbers and letters can be repeated. How many different VIN codes can there be? Write your answer in scientific notation; round the first factor to the hundredths.
Would the answer be: 3.56x10^14? I got this answer by doing 17 nPr 17
According to the condition you stated
36x36x36x26x26x10x10x36x10x36x10x10x10x10x10x10x10
= (36^5)(26^2)(10^10)
= 4.09 x 10^20
why did you multiply it 5, 2, and 10 times? like why is it 35^5, 26^2, and 10^10?
To find the number of different VIN codes, we need to analyze the possible options for each position.
Position 1: There are 36 options (26 letters + 10 numbers).
Position 2: There are 36 options.
Position 3: There are 36 options.
Position 4: There are 26 options (letters only).
Position 5: There are 26 options.
Position 6: There are 10 options (numbers only).
Position 7: There are 10 options.
Position 8: There are 36 options.
Position 9: There are 10 options.
Position 10: There are 36 options.
Positions 11-17: Each position has 10 options.
Now we can multiply all of these options together to find the total number of different VIN codes:
36 * 36 * 36 * 26 * 26 * 10 * 10 * 36 * 10 * 36 * 10 * 10 * 10 * 10 * 10 * 10 * 10
Simplifying this expression gives:
6,916,595,780,000,000
In scientific notation, this is:
6.92 x 10^15
Therefore, the correct answer is 6.92 x 10^15, not 3.56 x 10^14 as you calculated using permutation.