Question

Your answer is incorrect. Suppose that a "code" consists of 6 digits, none of which is repeated. (A digit is one of the 10 numbers 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 .) How many codes are possible?

Answer 1

Use factorials to solve this problem.

When you are choosing a number of digits from a set without repetition, you will use the following formula:

$\frac{n!}{(n-r)!}$

n represents the total amount of items in the set, and r represents the number of items you will take out.

There are 10 digits, and you are choosing sets of 6 digits for your code. Plug the values into the equation:

$\text{n = 10, r = 6}$

$\frac{10!}{(10-6)!} = \frac{10!}{4!} = \boxed{151,200}$

There are 151,200 different 6-digit codes possible.

Answer 2

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