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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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Four toys—a stuffed animal, a ball, a toy car, and a doll—are to be distributed among three children—Jasmine, Katey, and Leah. If the toys are to be distributed in such a way that each child receives at least one toy, how many such distributions are possible?
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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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How many points (r, s) can be formed so that r < s, and that the x and y-coordinates of the point are both selected from odd integers between 1 and 399, inclusive?
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Four guests A, B, C and D have to be assigned into three different rooms (one double room and two single rooms) 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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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 and 2 pairs of shoes. She could choose 1 jacket, 1 pant and 1 pair of shoes every day. However, 1 jacket and 1 pant don`t match, so they cannot be selected together. In such circumstance, for how many days can she wears differently?
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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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In how many ways can 4 kids (2 boys and 2 girls) be selected out of 5 couples of boy-girl twins such that no kids are selected from the same couple?
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A password is formed by 5 digits, including a "1", two "2" and two "4". How many different passwords can be formed?
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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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What is the probability of selecting two socks of the same color when selecting two socks out of 5 pairs of different colors of socks (each pair of socks have the same color)?
Give your answer as a fraction.
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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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