Question

In a certain country, the car license plate formed by 4 numbers from the digits 1-9 followed by 3 letters from the alphabet. How many license plates can be formed if neither the digits nor the letters are repeated?

Answer 1

Answer:

78,624,000 license plates

Step-by-step explanation:

For each of the 4 numbers, we have the following possibilities:

First number: 10 digits possible

Second number: 9 digits possible (one used)

Third number: 8 digits possible (two used)

Fourth number: 7 digits possible (three used)

For each of the 3 letters, we have the following possibilities:

First letter: 26 digits possible

Second letter: 25 digits possible (one used)

Third letter: 24 digits possible (two used)

The total number of license plates is the product of all these possibilities:

Number of plates = 10 * 9 * 8 * 7 * 26 * 25 * 24 = 78,624,000 license plates