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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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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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How many integers between 1 and $$10^{21}$$ are such that the sum of their digits is 2?
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Three typists work for four different companies. Each company has one document, and each document can be assigned to any of the three typists. What is the probability that three typists all receive documents?
Give your answer as a fraction.
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Point A (a, b) is in the xy-plane where both a and b are positive integers. What is the number of point A such that a+b < 200?
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Four guests A, B, C and D have to be assigned into three different double rooms (at least one guest has to be assigned to each room) such that A and B won`t have to stay in the double room at the same time. How many ways in total can they be assigned into these rooms?
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Linda has 4 jackets, 3 pants, 2 pairs of shoes and 4 scarfs. She could choose 1 jacket, 1 pant and 1 pair of shoes every day. However, she could either wear 1 of the 4 scarfs or just wear no scarf. In such circumstance, for how many days can she wears differently?
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In how many different ways can 3 identical green shirts and 3 identical red shirts be distributed among 6 children such that each child receives a shirt?
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The 8 items A, B, C, D, E, F, G, and H are to be displayed on a straight line. In how many ways can the items be displayed if item B must be placed in any position that is to the right of item A, and item C must be placed in any position that is to the right of B?
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If one number is chosen at random from the first 1,000 positive integers, what is the probability that the number chosen is a multiple of both 2 and 8?
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A box contains 6 cards, numbered 1, 2, 3, 4, 5, and 6, respectively. If one of the 6 cards is to be selected at random, what is the probability that the number on the card selected will be greater than 3, or even, or both?
Give your answer as a fraction.
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If all the digits of a three-digit integer are divisible by 3, then what is the probability that the tens digit of the integer is an odd number while the hundreds digit is an even number?
Give your answer as a fraction.
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In a group of 10 employees, 4 are good at computer. If 3 employees are randomly selected from the group, what is the probability that at least 2 employees selected are good at computer?
Give your answer as a fraction.
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Set={2, 3, 5, 6, 9, 10}
When selecting two different numbers from the set, what is the probability that the product of the two selected numbers is less than 50?
Give your answer as a fraction.
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What is the probability that the tens digit of the selected number is even when randomly selecting a number from all the two-digit odd integers?
Give your answer as a fraction.
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What is the probability that the number is more than 3,000 when forming four-digit integers out of 1, 2, 3 and 4 (no repeated number can be used)?
Give your answer as a fraction.
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If two numbers are randomly selected from positive integers from 1 to 10 such that no number is selected twice, what is the probability that the difference of the two selected numbers is 1?
Give your answer as a fraction.
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