How many ways at least

If there are 25 cars of this type, how many choices are available for transport? If there are 25 cars of this type, how many ways can they be loaded onto the truck for transport? Fifteen have automatic transmission. Twelve have leather seats.

Ten cars have both automatic transmission and leather seats. If there are no restrictions, how many different social security numbers are possible?

Four of the drives are defective. A sample of 2 are selected randomly. How many ways can the following be done? How many ways can we select. Hanley Rd, Suite St. Louis, MO Subject optional. Email address: Your name:. Possible Answers: 8. Correct answer: 5.

Explanation : The fundamental counting principle says that if you want to determine the number of ways that two independent events can happen, multiply the number of ways each event can happen together. Report an Error. Possible Answers: Correct answer: Explanation : This is a permutation problem, because we are looking for the number of groups of winners.

Explanation : Since this a combination problem and we want to know how many different ways the cookies can be created we can solve this using the Fundamental counting principle. Possible Answers: million. Correct answer: 18 million. Explanation : The total number of possible combinations of a series of items is the product of the total possibility for each of the items.

Explanation : The first person holds 7 hands. Explanation : There are 5x4x3 ways to arrange 5 flavors in 3 ways. Explanation : You have 3 possible types of bread, 2 possible types of meat, and 2 possible types of cheese. Copyright Notice. Lynne Certified Tutor. Patricia Certified Tutor. Compute the probability of randomly guessing the answers and getting exactly 9 questions correct. In many card games such as poker the order in which the cards are drawn is not important since the player may rearrange the cards in his hand any way he chooses ; in the problems that follow, we will assume that this is the case unless otherwise stated.

Thus we use combinations to compute the possible number of 5-card hands, 52 C 5. This number will go in the denominator of our probability formula, since it is the number of possible outcomes.

For the numerator, we need the number of ways to draw one Ace and four other cards none of them Aces from the deck. Since there are four Aces and we want exactly one of them, there will be 4 C 1 ways to select one Ace; since there are 48 non-Aces and we want 4 of them, there will be 48 C 4 ways to select the four non-Aces.

The solution is similar to the previous example, except now we are choosing 2 Aces out of 4 and 3 non-Aces out of 48; the denominator remains the same:. It is useful to note that these card problems are remarkably similar to the lottery problems discussed earlier. Compute the probability of randomly drawing five cards from a deck of cards and getting three Aces and two Kings. Suppose you have a room full of 30 people. What is the probability that there is at least one shared birthday? Take a guess at the answer to the above problem.

Suppose three people are in a room. Viewed 23k times. Vikram Vikram 5, 8 8 gold badges 37 37 silver badges 60 60 bronze badges. Add a comment. Active Oldest Votes.

The easiest way is to count the total and subtract the complement. Graham Kemp Graham Kemp k 6 6 gold badges 45 45 silver badges bronze badges.

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