Shannon was born on 12/21/1982. How many eight digit codes could she make using the digits in her birthday?

Explanation:

Ignoring the slashes, there are 8 digits here. If we could tell those '1's and '2's apart, then we'd have 8! = 40,320 different codes. The exclamation mark indicates a factorial.

However, the '1's and '2's are indistinguishable. We have to divide by a!*b! = 3!*3! = 6*6 = 36 to account for this.

The a! = 3! = 6 is from the fact we have 3 copies of '1'.

The b! = 3! = 6 is from the fact we have 3 copies of '2'

Dividing by 36 gets us (40,320)/36 = 1120

the discriminant is 64 + 4*1*12 = 112

this is prime.

step-by-step explanation:

you probably already have the answer but anyways it's b. 15.0

step-by-step explanation: