Question

what is a permutation?

Answer 1

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

Answer 2

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

Answer 3

let us provide an example that uses fundamental counting principle

Answer 4

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

Answer 5

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

Answer 6

that's just a three letter word.

Answer 7

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

Answer 8

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

Answer 9

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.

Answer 10

without repetition:
\(\large _nP_n \): number of permutations of "n" things taken "n" at a time.

\(\large _nP_n = n! \)

Answer 11

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).

Answer 12

\(\sf P:20; VP: 19; S:18\)
\(20 \times 19 \times 18 = 6840\)

Permutations of "n" elements taken "r" at a time.
\(\large _nP_r = \frac{n!}{(n-r)!} = \frac{20!}{(20-3)!} = 6840 \)

Answer 13

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