Question

Shannon was born on 09/09/1990. How many eight-digit codes could she make using the digits in her birthday?

Answer 1

Step-by-step explanation

The birth date of Shannon is 09/09/1990

Generally, the number of digits present in her birth date is n = 8

Looking at the date we can see that 0 is repeated 3 times and 9 is repeated 4 times. Therefore, the total number eight-digit code that she could make using her birthday given the total number of digits that make up her birth date is

`n!=8!`

but given that digit, 0 repeated itself 3 times, and 9 repeated itself 4 times, then the total number of eight-digit codes that she could make using her birthday will be mathematically evaluated as

`(8!)/(3!*4!)=(8*7*6*5*4!)/(4!*3*2*1)=8*7*5=280`

Answer: 280