508cb39a-63d8-47ea-aa92-22039cc5a199 6 4 5 false false 0 decimal

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Permutations

n r P n! n r - (! / :

62 P 30

There are 30 permutations of 6 objects taken 2 at a time

Example: A specific program requires the user to enter a 5-digit password. The digits cannot repeat and can be any five digits 1,2,3,4,7,8, and 9. How many different passwords are possible? 7 Objects taken 5 at a time:

75 P 2520

different passwords are possible

Combinations Example: A club with ten menbers wants to choose a committee of four members. Six of the members are women, and four are men. How many different committes are possible?

n r C n! n r - (! (r! * / :

104 C 210

There are 210 ways to chooses a committee of four when order is not importaint

If the comittee is chosen randomly, what is the probability that two members of the committee are men?

42 C 6

6 ways to chooses two men randomly

62 C 15

15 ways to chooses two women randomly

Counting Principle, there are 6 * 15 or 90 ways to choose a committee with two men and two women. Probability (2 men and 2 women) = (number of favorable outcomes)/ (number of possible outcomes)

90210 / % 43