Permutations and Combinations questions
785 published questions with worked solutions.
- Given S= (x, y, z) R^3 : xyz=210, x<y<z, where x, y, z are positive integers What is the total number of elements in S?
- Let A and B be the sets having only 2 and 3 elements respectively. What is the total number of mappings from A to B?
- In how many ways can a team of 5 players be selected from 8 players so as not to include a particular player?
- Let S= 2, 3, 4, 5, 6, 7, 9 . How many different 3-digit numbers (with all digits different) from S can be made which are less...
- Suppose 20 distinct points are placed randomly on a circle. Which of the following statements is/are correct? 1. The number of...
- Consider the digits 3, 5, 7, 9. What is the number of 5-digit numbers formed by these digits in which each of these four digits...
- How many distinct matrices exist with all four entries taken from 1, 2 ?
- Seven white balls and three black balls are randomly placed in a row. What is the probability that no two black balls are placed...
- An engineer is required to visit a factory for exactly four days during the first 15 days of every month and it is mandatory that...
- In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these...
- Let S_1 = (i, j, k) : i, j, k 1, 2, , 10 , S_2 = (i, j) : 1 i < j + 2 10, i, j 1, 2, , 10 , S_3 = (i, j, k, l) : 1 i < j < k < l,...
- The number of 4-digit integers in the closed interval [2022, 4482] formed by using the digits 0, 2, 3, 4, 6, 7 is _____.
- Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many...
- A group of 9 students, s_1, s_2, , s_9, is to be divided to form three teams X, Y, and Z of sizes 2, 3, and 4, respectively....
- The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red...
- A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168, then b + 3g is...
- Let S be the set of all passwords which are six to eight characters long, where each character is either an alphabet from A, B,...
- The number of ways to distribute 30 identical candies among four children C_ 1 , C_ 2 , C_ 3 and C_ 4 so that C_ 2 receives...
- The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is
- The number of matrices of order 3 3, whose entries are either 0 or 1 and the sum of all the entries is a prime number, is _____.
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