150k views
5 votes
Shannon was born on 12/21/1982. How many eight digit codes could she make using the digits in her birthday?

1 Answer

7 votes

Answer: 1120

============================================================

Step-by-step 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

User Meaku
by
6.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories