P Permutations versus Combinations

4! is read as 4 factorial and is... 4 x 3 x 2 x 1. It equals 24. 3! = 5! is read as 5 factorial and is... 5 x 4 x 3 x 2 x 1. It equals 120. 7! = 7 x 6 x 5 x • • • 3! = x x 0! is read as 0 factorial and equals 1. 3! is read as 3 factorial and is... 3 x 2 x 1. It equals 6. 4! = x x x Permutations - order matters like combination locks
Of n things taken r at a time. n P r = or n count down r times (n-r)! n! N is the number of items being arranged in lots of r.
How many items are there to pick from ? n P r =
or n count down r times (n-r)! n! N is the number of items being arranged in lots of r.
How many items are in each group? items n P r =
or n count down r times (n-r)! n!
Permutations - order matters like combination locks - Of n things taken r at a time. n P r = 6 x 5
(n-r)! n! or 6 P 2 = (6-2)! 6! Permutations - order matters like combination locks - Of n things taken r at a time. n P r 6 x 5 x 4 = = or n count down r times (n-r)! n! 6 P 3 = (6-3)! 6! Permutations - order matters like combination locks - Of n things taken r at a time. n P r 7 x 6 x 5 = = or n count down r times (n-r)! n! 7 P 3 = (7-3)! 7! Permutations - order matters like combination locks - Of n things taken r at a time. 5 P 2 = or 5 x 4 = 20 (5-2)! 5! = 5! ! Permutations - order matters like combination locks - Of n things taken r at a time. 8 P 2 = count down 2 spots 8 x 7 = (8-2)! 8! = 8! ! Permutations - order matters like combination locks - Of n things taken r at a time. 8 P 3 x x = 336 = count down 3 spots (8-3)! 8! = 8! ! Permutations - order matters like combination locks - Of n things taken r at a time. 8 P 4 x x x = 1680 = count down 4 spots (8-4)! 8! = 8! ! Combinations - order does not matter - like ordering a pizza with multiple toppings - of n things taken r at a time. n n count down r times C r = r! (n-r)! n! r! or Combinations - order does not matter - like ordering a pizza with multiple toppings - of n things taken r at a time. n n count down r times would be like the number of toppings to pick from C r = r! (n-r)! n! r! or Combinations - order does not matter - like ordering a pizza with multiple toppings - of n things taken r at a time. n n count down r times C is like the number of toppings you can select r = r! (n-r)! n! r! or Combinations - order does not matter - like ordering a pizza with multiple toppings - of n things taken r at a time. or n count down r times 6 C 2 = r! 2! (6-2)! 6! = (2•1) 6•5•4•3•2•1 3 6 x 5 2 x 1 (4•3•2•1) = Combinations - order does not matter - like ordering a pizza with multiple toppings - of n things taken r at a time. or n count down r times 6 C 3 = r! 3! (6-3)! 6! = 6 x 5 x 4 3 x 2 x 1 (3•2•1) 6•5•4•3•2•1 (3•2•1) = Combinations - order does not matter - like ordering a pizza with multiple toppings - of n things taken r at a time. or n count down r times 7 C 3 = r! 3! (7-3)! 7! = (3•2•1) 7•6•5•4•3•2•1 7 x 6 x 5 3 x 2 x 1 (4•3•2•1) = Combinations - order does not matter - like ordering a pizza with multiple toppings - of n things taken r at a time. 5 C 2 = 2! (5-2)! 5! or n count down r times r! Combinations - order does not matter - like ordering a pizza with multiple toppings - of n things taken r at a time. 8 C 2 = 2! (8-2)! 8! or n count down r times r! Combinations - order does not matter - like ordering a pizza with multiple toppings - of n things taken r at a time. 5 C 3 = 3! (5-3)! 5! or n count down r times r! Where a permutation of 3 things taken in lots of 3 has 6 choices (see choices below) because order matters, a combination of 3 things taken in lots of 3 has choice(s) because order does not matter. ABC ACB BAC BCA CAB CBA Possible choices for a P 3 3 Where a permutation of 3 things taken in lots of 2 has 6 choices (see choices below) because order matters, a combination of 3 things taken in lots of 2 has choice(s) because order does not matter. AB AC BA BC CA CB Possible choices for a P 3 2 Where a combination of 4 things taken in lots of 2 has 6 choice(s) because order does not matter a permutation will have more choices as when the order changes it makes a new set. The permutation of 4 things taken in lots of 2 will have choices. 1) AB = BA 2) AC = CA 3) AD = DA Possible choices for a C 4) BC = CB 5) BD = DB 6) CD = CD 4 2 Runners finishing a race Order matters as in (AB ≠ BA) Permutation Order doesn't matter as in (AB = BA) Combination Four people applying for the same two jobs Order matters as in (AB ≠ BA) Permutation Order doesn't matter as in (AB = BA) Combination Four people applying for two different jobs Order matters as in (AB ≠ BA) Permutation Order doesn't matter as in (AB = BA) Combination Your locker combination Order matters as in (AB ≠ BA) Permutation Order doesn't matter as in (AB = BA) Combination Ordering pizza with several toppings Order matters as in (AB ≠ BA) Permutation Order doesn't matter as in (AB = BA) Combination Applying for the same jobs on a year book staff Order matters as in (AB ≠ BA) Permutation Order doesn't matter as in (AB = BA) Combination Four people applying for different positions on the yearbook staff Order matters as in (AB ≠ BA) Permutation Order doesn't matter as in (AB = BA) Combination Running for office - first place votes is President, second place, Vice President, etc. Order matters as in (AB ≠ BA) Permutation Order doesn't matter as in (AB = BA) Combination |

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