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In a city election, there are 2 candidates for mayor, and 3 for supervisor. Use a tree diagram to find the number of ways to fill the two offices.
There are 4 roads from Town A to Town B, 2 roads from Town B to Town C. Use a tree diagram to find the number of ways one can travel from Town A to Town C.
8
Brown Home Construction offers a selection of 3 floor plans, 2 roof types, and 2 exterior wall types. Use a tree diagram to determine the number of possible homes available.
For lunch, a small restaurant offers 2 types of soups, three kinds of sandwiches, and two types of soft drinks. Use a tree diagram to determine the number of possible meals consisting of a soup, sandwich, and a soft drink.
12
A California license plate consists of a number from 1 to 5, then three letters followed by three digits. How many such plates are possible?
A license plate consists of three letters followed by three digits. How many license plates are possible if no letter may be repeated?
15,600,000
How many different 4-letter radio station call letters can be made if the first letter must be K or W and none of the letters may be repeated?
How many seven-digit telephone numbers are possible if the first two digits cannot be ones or zeros?
6,400,000
How many 3-letter word sequences can be formed using the letters $\left\{a,b,c,d\right\}$ if no letter is to be repeated?
A family has two children, use a tree diagram to determine all four possibilities.
BB, BG, GB, GG
A coin is tossed three times and the sequence of heads and tails is recorded. Use a tree diagram to determine the different possibilities.
In how many ways can a 4-question true-false test be answered?
16
In how many ways can three people be made to stand in a straight line?
A combination lock is opened by first turning to the left, then to the right, and then to the left again. If there are 30 digits on the dial, how many possible combinations are there?
27,000
How many different answers are possible for a multiple-choice test with 10 questions and five possible answers for each question?
Do the following problems using permutations.
How many three-letter words can be made using the letters $\left\{a,b,c,d,e\right\}$ if no repetitions are allowed?
60
A grocery store has five checkout counters, and seven clerks. How many different ways can the clerks be assigned to the counters?
A group of fifteen people who are members of an investment club wish to choose a president, and a secretary. How many different ways can this be done?
210
Compute the following.
$\mathrm{9P2}$
$\mathrm{6P4}$
$\mathrm{8P3}$
$\mathrm{7P4}$
In how many ways can the letters of the word CUPERTINO be arranged if each letter is used only once in each arrangement?
362,880
How many permutations of the letters of the word PROBLEM end in a vowel?
How many permutations of the letters of the word SECURITY end in a consonant?
25,200
How many permutations of the letters PRODUCT have consonants in the second and third positions?
How many three-digit odd numbers are there?
In how many different ways can five people be seated in a row if two of them insist on sitting next to each other?
48
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