An eyewitness to a crime said that the license plate of the getaway car began with the letters T an V, but he could not remember the order. The rest of the plate had the numbers 7,4, and 5 , but again he did not recall the order. How many license plates must the police investigate to find the car?

12 possible arrangements.

Step-by-step explanation:

there are 2 possible position for the first letter.

there is 1 possible position for the second letter.

there are 3 possible position for the first number.

there are 2 possible position for the second number.

there is 1 possible position for the third number.

the total possibilities are 2 * 1 * 3 * 2 * 1 = 12

Or we can solve by saying:

There are 2 letters T and V that can be in the first two positions in any order that is 2!, and there are 3 numbers (7,4 and 5) that can be in the last 3 positions in any order that is 3!.

Therefore possible arrangement

2! * 3! = 2 * 1 * 3 * 2 * 1 = 12

12 possible arrangements.