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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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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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A certain band will perform 15 different songs in random order, and no song will be performed twice. If 9 of the songs are new, what is the probability that the first 2 songs that the band performs will both be new?
Give your answer as a fraction.
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Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?
Give your answer as a fraction.
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There are 10 pens in a box, and 2 of the pens are defective. If 2 pens are to be selected at random from the box without replacement, what is the probability that neither will be defective?
Give your answer as a fraction.
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What is the probability that someone randomly selects a number from 100 to 159 inclusive such that the tens digit of the selected number is no more than 3 and the units digit of the selected number is no more than 4?
Give your answer as a fraction.
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Two companies, $$C_1$$, and $$C_2$$, are participating in a fund-raising activity along with 8 other companies. Of the 10 companies, a group of 4 companies will be chosen to receive an award. Of all the possible choices of groups of 4 companies that will receive an award, how many choices include both companies $$C_1$$ and $$C_2$$?
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From a group of 100 people including Alice and Bob, 40 people are to be randomly selected at the same time to win movie tickets. What is the probability that both Alice and Bob will be selected to win movie tickets?
Give your answer as a fraction.
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