Question

Three friends will run race. If three friends no ties, in how many distinct order can these 3 friends finish the race?​

Answer 1

Answer:  6 different ways

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Explanation:

Let's name the friends A, B, C

If person A is first, then B or C could be second and third.

So we have ABC or ACB as two possible outcomes.

If B is first, then either A is second or C is second. Meaning we have BAC or BCA.

If C is first, then we have CAB or CBA

Overall here are the 6 different ways to have the runners finish

1. ABC ... A is first
2. ACB ... A is first
3. BAC ... B is first
4. BCA ... B is first
5. CAB ... C is first
6. CBA ... C is first

Note how for the first slot we have 3 ways to pick the winner. Then after that selection is made, we have 2 choices left, then 1 choice for third place. Therefore, 3*2*1 = 6 different outcomes are possible.

We can use the factorial operation on the calculator to do this with one button press, so we'd say 3! = 6. The exclamation mark means "multiply from 3 down to 1, counting down the whole time".

Another example of a factorial is:

5! = 5*4*3*2*1 = 120