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Combinatorics | Number Theory
A man has 3 different suits, 4 different shirts and 5 different pairs of shoes. In how many different ways can this man wear a suit, a shirt and a pair of shoes?
Combinatorics | Number Theory
There are 3 different roads from city A to city B and 2 different roads from city B to city C. In how many ways can someone go from city A to city C passing by city B?
Combinatorics | Number Theory
A student can select one of 6 different mathematics books, one of 3 different chemistry books and one of 4 different science books. In how many different ways can a student select a book of mathematics, a book of chemistry and a book of science?
Combinatorics | Number Theory
In a certain country telephone numbers have 9 digits. The first two digits are the area code (03) and are the same within a given area. The last 7 digits are the local number and cannot begin with 0. How many different telephone numbers are possible within a given area code in this country?
Combinatorics | Number Theory
To buy a computer system, a customer can choose one of 4 monitors, one of 2 keyboards, one of 4 computers and one of 3 printers. Determine the number of possible systems that a customer can choose from.
Combinatorics | Number Theory
Use the method of contradiction to prove that √5 is not a rational number.
Combinatorics | Number Theory
Let p(x): x is mammal and q(x): x is animal. Translate the following in English: (∀x)(q(x)∧(∼p(x))).
Combinatorics | Number Theory
a. In how many different ways you put 20 equal balls, into two numbered boxes?
c. What if you have 20 equal balls, three numbered boxes, and you want to place at least 2 balls in the first box, and no more than 10 balls in the last box?
c. What if you have 20 equal balls, three numbered boxes, and you want to place at least 2 balls in the first box, and no more than 10 balls in the last box?
Combinatorics | Number Theory
A password for the computer is a string of digits and/or letters. The password must obey the following rules:
a. The length of the password must be exactly 8 characters
b. The password must contain at least one digit, and no more than three digits.
What is the number of different passwords you can form?
a. The length of the password must be exactly 8 characters
b. The password must contain at least one digit, and no more than three digits.
What is the number of different passwords you can form?
Combinatorics | Number Theory
There are 5 chairs in a row, and three people. In how many ways can you place the people on the chairs? (each person must occupy exactly one chair, so that two chairs will remain free.)
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