A local hockey club is setting up an online system to register its players. Seven-character passwords will be assigned to each player, all starting with the letter S to indicate the home club. The other characters in the password are made up of the numerals 4 through 9, and no digit can be repeated. How many passwords can the hockey club create?a.40,320b.720c.5,040d.362,880
Question
A local hockey club is setting up an online system to register its players. Seven-character passwords will be assigned to each player, all starting with the letter S to indicate the home club. The other characters in the password are made up of the numerals 4 through 9, and no digit can be repeated. How many passwords can the hockey club create?a.40,320b.720c.5,040d.362,880
Solution
The first character of the password is always 'S', so we don't have any choices for it.
For the second character, we have 6 choices (4, 5, 6, 7, 8, 9).
For the third character, we have 5 choices left (since we can't repeat a digit).
For the fourth character, we have 4 choices left.
For the fifth character, we have 3 choices left.
For the sixth character, we have 2 choices left.
For the seventh character, we have 1 choice left.
So, the total number of passwords is 1 (for the first character 'S') times 6 (for the second character) times 5 (for the third character) times 4 (for the fourth character) times 3 (for the fifth character) times 2 (for the sixth character) times 1 (for the seventh character).
This is 1654321 = 720.
So, the correct answer is b. 720.
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