Shannon was born on 04/02/2004. How many eight-digit codes could she make using the digits in her birthday?

The number of eight digit codes she can make using the digits in her birthday is; 420 eight digit codes

The 8 digits code of her birth date are;

0, 4, 0, 2, 2, 0, 0, 4

Now, since there are 8 digits, then number of ways of arranging the 8 digits is 8!

Since there are some repetitions, then we have to consider the permutations for them too.

There are four 0's which is 4!

There are two 2's which is 2!

There are two 4's which is 2!

Thus, number of 8 digit codes she can make using the digits on her birthday is;

8!/(4! × 2! × 2!) = 420 eight digit codes

Read more about permutations and combinations at; link

420 different codes.

Step-by-step explanation:

We have eight digits, {0, 0, 0, 0, 2, 2, 4, 4}

For the first digit of the code, we will have 8 options.

For the second we will have 7 options (because we already took one)

for the third one we will have 6 options, and so on.

for the fourth, we will have 5 options

for the fifth, there are 4 options.

for the sixth, there are 3 options.

for the seventh, there are 2 options.

And for the last, there is only one option.

The total number of combinations will be equal to the product between the numbers of options for each digit, then we will have:

C = 8*7*6*5*4*3*2*1

But there is something more, the zeros can permute and will give the same code (So we are counting the same code several times), we have 4 zeros, then the number of permutations of the zeros is:

4*3*2*1  = 24

the 4's also are repeated, two times in this case, the number of permutations is:

2*1 = 2

And the 2's also are repeated, also two times, the number of permutations is:

2*1 = 2

Because we do not want to count these repetitions, we need to divide the total number of combinations by these 3 numbers of permutations

This means that we need to divide the number of different combinations will be:

c = (8*7*6*5*4*3*2*1)/(24*2*2) = 420

So we can conclude that there are 420 different codes.

$54.99

step-by-step explanation:

$54.99 includes 500 min. if she does not exceed 500 min then her bill is $54.99