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Five gift cards will be distributed among 10 people so that no person receives more than one gift card. The gift cards consist of one $100 gift card, one $50 gift card, one $25 gift card and two $10 gift cards. How many different distributions of the five gift cards among the 10 people are possible if the two $10 gift cards are considered to be identical?
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A knockoff website requires users to create a password using letters from the word MAGOSH. If each password must have at least 4 letters and no repeated letters are allowed, how many different passwords are possible?
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A four-digit integer is formed out of 0, 1, 2 and 3 (the same number could be used by more than once) where the sum of all the digits is 3. How many integers in total meet the requirement?
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In how many ways can a 5-person committee can be formed out of 6 professors, 3 managers and 4 coordinators such that Dr. W, one of the professors, and Ms. M, one of the managers, are both selected?
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From a group of 8 people, it is possible to create exactly 56 different k-person committees. Which of the following could be the value of k ?
Indicate all such values.
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How many factors of 210 can be expressed as the product of two prime numbers?
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How many three-digit integers between 100 and 900, inclusive, are out there where the sum of their first two digits and last two digits are both 7?
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Four different persons will be selected from 2 men and 5 women to serve on a committee. If at least 1 man and 1 woman must be among thoses selected, how many different selections of the 4 persons are possible?
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How many even double-digit integers can be formed out of six integers from 1 to 6 such that no repeated numbers are used?
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Five identical balls need to be put into three different boxes. At least one ball should be included in each box. How many ways can these balls be arranged?
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Six identical balls need to be put into four different boxes. At least one ball should be included in each box. How many ways can these balls be arranged?
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How many positive integers can be expressed as a product of two or more of the prime numbers 5, 7, 11, and 13 if no one product is to include the same prime factor more than once?
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A reading list for a humanities course consists of 10 books, of which 4 are biographies and the rest are novels. Each student is required to read a selection of 4 books form the list, including 2 or more biographies. How many selections of 4 books satisfy the requirements?
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There are 4 fiction books and 6 non-fiction ones, while 3 of the non-fiction are biographies. Now choose 3 books from the total 10 books. What is the probability of at least one fiction and no more than 1 biography are selected?
Give your answer as a fraction.
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To set a three-letter password for a website, a person selects two letters from the 26 alphabet and use one letter twice. How many different passwords are possible?
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In how many different ways can 3 boys and 3 girls be seated in a row of 6 chairs such that the girls are not separated, and the boys are not separated?
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In how many ways can three couples sit in a row such that each couple sit together?
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On a bookshelf, Pat arranges 7 different books: 2 history books, 3 philosophy books, and 2 science books. If Pat arranges the books so that the history books are next to each other, the science books are next to each other, and the philosophy books are next to each other, how many different arrangements are possible?
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Sid intended to type a seven-digit number, but the two "3" he meant to type did not appear. What appeared instead was the five-digit number 52115. How many different seven-digit numbers could Sid have meant to type?
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A fair coin is tossed 6 times. What is the probability of getting no any two heads on consecutive tosses?
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