The number of eight-digit codes could she make using the digits in her birthday is 1120 digits
Since the order of the arrangement of the digits matter, we use permutations
Permuations are the number of ways of arranging n objects in r ways. It is given as ⁿPₓ = n(n - 1)(n -2)...(n - x + 1). If we have r identical objects out of n objects, the number of arrangements are n!/r!
Now, since in the date Lucy was born 11/09/1993 has eight digits, we need to find the number of permutations the eight digits of her birthday to form an eight digit code.
Since there are 8 digits, three one's, three nine's, one 1 and one 3.
The number of permutations of these digits in an eight digit code, since we have repeated objects are n = 8!/3!3!1!1!
= 40320/6 × 6 × 1 × 1
= 40320/36
= 1120 digits
So, the number of eight-digit codes could she make using the digits in her birthday is 1120 digits
Learn more about permutations here:
https://brainly.com/question/5708836
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