You need to have a password with 6
letters followed by 3
odd digits between 0
and 9
, inclusive. If the characters and digits cannot be used more than once, how many choices do you have for your password?
To calculate the number of choices for the password, we can break it down into two parts: the letters and the odd digits.
For the letters, we have 26 choices for the first letter, 25 choices for the second letter (since we cannot repeat the first letter), and so on. This gives us 26 x 25 x 24 x 23 x 22 x 21 = 26P6 = 26! / (26-6)! = 26 x 25 x 24 x 23 x 22 x 21 = 165,765,600 choices for the letters.
For the odd digits, we have 5 choices (1, 3, 5, 7, 9) for the first digit, 4 choices for the second digit (since we cannot repeat the first digit), and 3 choices for the third digit. This gives us 5 x 4 x 3 = 60 choices for the odd digits.
Multiplying the number of choices for the letters and the odd digits gives us the total number of choices for the password:
165,765,600 x 60 = 9,946,536,000
Therefore, you have 9,946,536,000 choices for your password.