Jay bought a new car in New York where a license plate can be created with alphabets A, B, C, D, E, W, X, Y, Z and numbers 0 to 9. He can either select a normal license plate or a VIP license plate. The VIP license plate begins with 2 alphabets followed by 2 numbers with repetition allowed. The normal license plate begins with 1 numbers followed by 3 alphabets without repetition.In how many ways can he select the license plate(normal or VIP)?
Question
Jay bought a new car in New York where a license plate can be created with alphabets A, B, C, D, E, W, X, Y, Z and numbers 0 to 9. He can either select a normal license plate or a VIP license plate. The VIP license plate begins with 2 alphabets followed by 2 numbers with repetition allowed. The normal license plate begins with 1 numbers followed by 3 alphabets without repetition.In how many ways can he select the license plate(normal or VIP)?
Solution
To solve this problem, we need to calculate the number of ways to create a VIP license plate and a normal license plate separately, and then add them together.
For the VIP license plate, there are 9 options for the first alphabet (A to E, W to Z), 9 options for the second alphabet (since repetition is allowed), 10 options for the first number (0 to 9), and 10 options for the second number (since repetition is allowed). So the total number of ways to create a VIP license plate is 9 * 9 * 10 * 10 = 8100.
For the normal license plate, there are 10 options for the number (0 to 9), 9 options for the first alphabet (A to E, W to Z), 8 options for the second alphabet (since repetition is not allowed), and 7 options for the third alphabet (since repetition is not allowed). So the total number of ways to create a normal license plate is 10 * 9 * 8 * 7 = 5040.
So the total number of ways to select a license plate (either normal or VIP) is 8100 + 5040 = 13140.
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