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If the number of permutations of n objects taken r at a time is six times the number of combinations of n objects.
Suppose that a hand of 8 cards is dealt from a standard deck of cards. What is the probability that the hand has atleast one spade?
A student borrowed $4000 from a credit union toward purchasing a car. The interest rate on such a loan is 14% compounded quarterly.
Find the number of ways to put eight different books in five boxes, if no box is allowed to be empty.
There is a lottery in which 2000 individuals enter, and of these a set of 120 names will be randomly selected.
A rigid motion of a cube can be thought of either as a permutation of its 8 vertices or as a permutation of its 6 sides.
The committee will contain 2 democrats, 2 republicans, and 3 independents. In how many ways can we choose the committee?
In how many ways can a man divide 7 gifts among his 3 children if the eldest is to receive 3 gifts and the others 2 each?
Baskin Robbins serves "31 Flavors" of ice cream. How many different two-scoop ice cream cones are possible if two different flavors.
There are six seats available in the car. In how many different ways can the six people be seated in the car if only three of them can drive?
You dream of someday winning the lottery (don't we all). You found out about a new lottery where the winning numbers are five different numbers.
A commitie of 12 members is headed by 3 directors of equal rank who are voted in. How many ways can the 3 directors be chosen from the 12 members?
During their first week of employment, half will be assigned to pick up garbage down town while the other half go on a training course.
I have 12 golfers total, and we are playing 6 rounds of golf with 4 golfers in each group. I want to try and have everybody play with each person at least once.
Eight Horses are entered in a race. In how many ways can they cross the finish line if ties are not allowed?
Which of the following is a valid probability distribution for a sample space S = {a,b,c,d}
Suppose that 30 different computer games and 20 different toys are to be distributed among 3 different bags of Christmas presents.
A group of people consists of 14 men and some women. One man and one woman can be selected in 252 ways.
A store selects four items from a selection of 6 items to arrange in a display. How many different arrangements are possible?
Would like to know how to figure this out. Is there a forumula? Does it involve factorials?
A television commercial for Little Caesars pizza announced that with the purchase of two pizzas, one would receive free any combination.
Given a two-step procedure where there are n1 ways to do Task 1, and n2 ways to do Task 2 after completing Task 1.
The student chooses two different main menu selections (must be different) and one salad?
If a committee varies its meeting days, how many meetings must it schedule before we can guarantee that at least two meetings will be held.
A seven-person committee composed of Adam, Betty, Cameron, David, Edward, Fritz, and Grace is to select a chairperson, secretary.