Permutations an...

If χ = {11, 2, 3, 4, 5}, then the number of different ordered pairs (Y, Z) that can formed such that Y ⊑ X, Z ⊑ χ and Y ∩ Z is empty, is

Statement I The number of ways distributing 10, identical balls in 4 distinct boxes such that no box is empty, is ⁹C₃ .
Statement II The number of ways of choosing any 3 places from 9 different places, is⁹C₃ .

A teacher takes 3 children from her class to the zoo at a time as often as she can, but she does not take the same three children to the zoo more than once. She finds that she goes to the zoo 84 times more that a particular child goes to the zoo. The number of children in her class is

A student is allowed to select atmost n books from a collection of (2 n+ 1)books. If the total number of ways in which he can select atleast one book is 225, then the value of n is

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is

In a shop, there are five types of ice-creams available. A child buys six ice-creams.
Statement I The number of different ways the child can buy the six ice-creams, is ¹⁰C₅
Statement II The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A's and 4 B's in a row.

The set S = 11, 2, 3, ... , 121 is to be partitioned into three sets A,B,C of equal size.
Thus, A ∪ B ∪ C= S
A ∩ B = B ∩ C = A ∩ C = ∅.
The number of ways to partition S is

Out of 6 boys and 4 girls, a group of 7 is to be formed. In how many ways can this be done, if the group is to have a majority of boys ?

The number of rectangles that you can find on a chess board is

A letter lock consists of three rings marked with 15 different letters. If N denotes the number of ways in which it is possible to make unsuccessful attempts to open the lock, then