nincompoop
  • nincompoop
what is a permutation?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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UsukiDoll
  • UsukiDoll
permutation < -- order matters combination <-- order doesn't matter
UsukiDoll
  • UsukiDoll
it's like a license plate. only the first spot can occupy the letter A
nincompoop
  • nincompoop
let us provide an example that uses fundamental counting principle

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UsukiDoll
  • 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
nincompoop
  • nincompoop
i.e. List all permutations of the letters in the word CAT.
UsukiDoll
  • UsukiDoll
that's just a three letter word.
UsukiDoll
  • UsukiDoll
wait... three letters... that's 3 x 3 x 3 = 27 if we allow those letters to be repetitive though.
UsukiDoll
  • UsukiDoll
but there's no CCAT or anything like that .. that would be 4!/2!
nincompoop
  • 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.
nincompoop
  • nincompoop
without repetition: \(\large _nP_n \): number of permutations of "n" things taken "n" at a time. \(\large _nP_n = n! \)
nincompoop
  • 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).
nincompoop
  • nincompoop
\(\sf P:20; VP: 19; S:18\) \(20 \times 19 \times 18 = 6840\) Permutations of "n" elements taken "r" at a time. \(\large _nP_r = \frac{n!}{(n-r)!} = \frac{20!}{(20-3)!} = 6840 \)
nincompoop
  • nincompoop
The 7-digit phone numbers in a city all have 661 as the first three digits. How many different phone numbers are possible?

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