security codes are made of 3 letters followed by four single digit numbers

Question

security codes are made of 3 letters followed by four single digit numbers. How many different 7 character security codes can be made if none of the letters can repeat and the first digit must be odd?

Answer 1

Michael

You simply need to multiply the number of possibilities for each entry. You said the letters could not repeat, but I'm assuming the numbers can. So for the first letter, there are 26 possibilities. For the second there would be 25, and the third 24. Since the first number must be odd, there are only 5 possibilities. For the rest there would be 10 possibilities.

The computation would be:

 

26*25*24*5*10*10*10 = 78,000,000 codes

Answer 2

Number of choices for each place

1st: 26

2nd: 25

3rd: 24

4th: 5

5th: 10

6th: 10

7th: 10

 

78,000,000