Permutations!!!
Ex: Permutations of the letters in the word “cat” are: Cat cta act atc tca tac
The number of permutations of n objects is n!
The number of permutations of n objects taken r at a time nPr =
The number of permutations of n things with n1 repeats or n2 repeats is:
P =
Examples
A. The phone number example:
B. At the 1992 Olympic Games, eight women qualified for the women’s 400-meter finals in track and field. Only three women can win medals. How many different ways could the top three medal winners occur?
C. How many permutations are there for the word Mississippi?
Combinations
A selection without regard to order is called a combination:
The number of combinations of n things taken r at a time:
nCr =
Evaluate: 4C3 10C6
Examples
A. From a row of 8 different varieties of soup on a shelf, how many groups of 5 cans can be selected?
B. An ice cream shop has 8 different toppings from which to choose. This week, if you buy 3 toppings for your sundae, you get another topping free. How many different ways can the sundae be made?
C. From a group of 6 men and 4 women, how many committees of two men and two women can be formed?
D. A bag contains 4 green, 3 yellow and 6 white marbles. How many ways can 2 green, 1 yellow and 4 white marbles be chosen?