Permutations and Combinations questions
785 published questions with worked solutions.
- If ^ n+4 C_ n+1 - ^ n+3 C_ n =15(n+2), then n =
- 21 friends were invited for a party. Two round tables can accommodate 12 and 9 friends each. The number of ways of the seating...
- A family consisting of a mother, father and their 8 children (4 boys and 4 girls) are to be seated at a round table in a party....
- There are 11 points in a plane of which 5 points are collinear. Then the total number of distinct quadrilaterals with vertices at...
- The number of ways in which 6 boys and 4 girls can be seated around a round table such that 2 special boys and a special girl...
- If the number of 5-element subsets of the set A = a_1, a_2, , a_ 20 of 20 distinct elements is k times the number of 5-element...
- Statement 1: If A and B be two sets having p and q elements respectively, where q > p. Then the total number of functions from...
- The number of arrangements that can be formed from the letters a, b, c, d, e, f taken 3 at a time without repetition and each...
- If n = ^mC_2, then the value of ^nC_2 is given by
- If P(S) denotes the set of all subsets of a given set S, then the number of one-to-one functions from the set S = 1, 2, 3 to the...
- If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman,...
- Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be...
- Let X = 1, 2, 3, 4, 5 . The number of different ordered pairs (Y, Z) that can be formed such that Y X, Z X and Y Z is empty, is
- A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady, at least...
- On the sides AB, BC, CA of a △ABC, 3, 4, 5 distinct points (excluding vertices A, B, C ) are respectively chosen. The number of...
- An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in...
- 8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do not...
- Let N denote the set of all positive integers. Consider the sets A= 1,2,3,4,5 and B= 1,2,3,4,5,6,7 . Let S be the set of all...
- In the value of 100! the number of zeros at the end is
- The sum of all the proper divisors of 9900 is
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