Question

The access code for a​ car's security system consists of six digits. The first digit cannot be zero and the last digit must be odd . How many different codes are​ available? (Note that 0 is considered an even​ number.)

Answer 1

The access code for a car's security system consists of six digits. The first digit cannot be zero and the last digit must be odd. There are 450,000 different codes available.

Step-by-step explanation:

To determine the number of different codes available, we need to consider the restrictions given in the question. The first digit cannot be zero and the last digit must be odd.

For the first digit, we have 9 options (1 through 9) since it cannot be zero.

For the last digit, we have 5 options (1, 3, 5, 7, or 9) since it must be odd.

For the remaining four digits (digits 2 to 5), we have 10 options (0 to 9) for each digit since there are no restrictions.

Therefore, the total number of different codes available is 9 × 10 × 10 × 10 × 10 × 5 = 450,000.

Answer 2

67200

Step-by-step explanation:

We are given that the access code for a car's security system consist of six digits.

First digit cannot be zero and the last digit must be odd.

We have available digits which can used from 0 to 9.

We have to find the number of different codes are available without replacement.

Total odd digits=1,3,5,7,9=5

The sixth place place can be filled by number of ways=5

The first place can be filled by number of ways=8

The second place filled by number of ways=8

The third place can be filled by number of ways=7

The fourth place can be filled by number of ways=6

The fifth place can be filled by number of ways=5

Therefore, the total number of different codes are available=
`5* 8* 8* 7* 6* 5=67200`

Answer:67200