Final answer:
The number of possible passwords created from the phrase 'basketball22' is 119,750,400, considering the arrangement of the letters (with one letter 'b' repeated) and the numbers '22'. This is calculated using permutation formulas accounting for repeated elements.
Step-by-step explanation:
The number of possible passwords a basketball player can create from the arrangement of the numbers and letters in 'basketball22' is calculated by considering the permutations of the letters and numbers. The word 'basketball' contains 10 characters, including one repeated letter, 'b', and two instances of '2' in '22'. The formula for permutation when there are repetitions is given by n! divided by the factorial of each duplicate's occurrences.
In 'basketball22', we have:
- 9 distinct letters (b, a, s, k, e, t, b, a, l, l)
- 1 letter (b) repeating 2 times
- 2 occurrences of the number '2'
Using the permutation formula for repeated items:
The total permutations = 12! / (2! * 2!) = 479,001,600 / 4 = 119,750,400 possible passwords.