- #1

danago

Gold Member

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**To open a safe, 4 number buttons must be pressed, in the correct order. Over time, the 4 numbers buttons of the code fade. A thief notices the faded buttons, so knows that the code consists of those 4 numbers.**

How many possible codes are there?

How many possible codes are there?

4 numbers can be arranged in 4! different ways, so there are 24 different possible combinations.

**The safe owner decides that he wants to change the code. How many possible codes are possible if each code can contain only 1 of the 4 faded numbers?**

[tex]

^4 C_1 \times ^8 C_3 \times 4!=5376

[/tex]

Since there are two groups, faded and non faded. One is selected from the faded numbers, and 3 from the remaining 8 non faded. i then multiplied by 4! since there are 4! ways of arranging the 4 numbers.

The answer guide says this is wrong though. Is anybody able to explain where i went wrong in my reasoning?

Thanks,

Dan.