## nincompoop one year ago what is a permutation?

1. UsukiDoll

permutation < -- order matters combination <-- order doesn't matter

2. UsukiDoll

it's like a license plate. only the first spot can occupy the letter A

3. nincompoop

let us provide an example that uses fundamental counting principle

4. UsukiDoll

Two types of permutation Permutation with repetition A combination lock. It can be 222 Permutation without repetition You're competing at a track and field race. You can only be first,second or third. You can't occupy first and second at the same time

5. nincompoop

i.e. List all permutations of the letters in the word CAT.

6. UsukiDoll

that's just a three letter word.

7. UsukiDoll

wait... three letters... that's 3 x 3 x 3 = 27 if we allow those letters to be repetitive though.

8. UsukiDoll

but there's no CCAT or anything like that .. that would be 4!/2!

9. nincompoop

so without repetition, we have: $$3 \times 2 \times 1$$ since we have 3 letters, which corresponds to 3 events. Meaning in our first event, it does not matter if we picked C, A or T. Then for our second event, we have only 2 letters left, because we exclude the first event that occurred; then it follows that we have one event left for the third event.

10. nincompoop

without repetition: $$\large _nP_n$$: number of permutations of "n" things taken "n" at a time. $$\large _nP_n = n!$$

11. nincompoop

20 people are running for an office in an election. In how many ways can you choose a President (P), Vice President (VP), and Secretary (S).

12. nincompoop

$$\sf P:20; VP: 19; S:18$$ $$20 \times 19 \times 18 = 6840$$ Permutations of "n" elements taken "r" at a time. $$\large _nP_r = \frac{n!}{(n-r)!} = \frac{20!}{(20-3)!} = 6840$$

13. nincompoop

The 7-digit phone numbers in a city all have 661 as the first three digits. How many different phone numbers are possible?