Probability & Permutation — practice questions, page 3
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A bag contains 5 red, 4 green and 3 blue balls. Two balls are drawn at random without replacement.…In how many distinct ways can all the letters of the word PROBABILITY be arranged?In how many ways can the letters of the word COMPUTER be arranged so that all the vowels always…A committee of 5 members is to be formed from 6 men and 4 women. In how many ways can the…From a group of 5 boys and 4 girls, 3 students are selected at random for a quiz team. What is the…Two fair dice are thrown together. What is the probability that the sum of the numbers obtained is…Two fair dice are rolled together. What is the probability that the product of the two numbers…A fair die is rolled three times. What is the probability of getting at least one six?One card is drawn at random from a well-shuffled pack of 52 playing cards. What is the probability…Two cards are drawn one after another at random from a pack of 52 playing cards, without…A bag contains 6 white and 4 black balls. A ball is drawn at random, its colour noted, and it is…In how many ways can 8 friends be seated around a circular table, counting only the arrangements…Six people are to be seated around a circular table. In how many ways can this be done if two…In how many ways can 5 boys and 3 girls be arranged in a row so that no two girls stand next to…In how many different ways can the letters of the word LEADING be arranged so that the vowels…How many arrangements of all the letters of the word NUMBER begin with N and end with R?How many different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6 and 7 if no…Using the digits 1, 2, 3, 4 and 5, with repetition allowed, how many 3-digit numbers divisible by…How many 3-digit numbers divisible by 5 can be formed from the digits 0, 1, 2, 3, 4 and 5 if no…At a meeting every person shook hands exactly once with every other person present, and 66…A polygon has 12 sides. Counting the combinations of two vertices that are not adjacent, how many…In how many ways can 10 identical chocolates be distributed among 4 children if every child must…In how many ways can 5 different prizes be given away to 3 students, if each student is eligible…A box holds 5 red pens, 4 blue pens and 3 green pens, all distinguishable. In how many ways can 3…A committee of 5 is to be chosen from 7 men and 4 women. In how many ways can it be formed if it…
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