Permutations an...

Given:   $$\dfrac {20!}{18!}=380$$

In a class of 80 students it is found that 40 students like Tajmahal and 50 students like Charminar and 18 like both. Then the number of students who do not like neither are.

In a combination, the ordering of the selected objects is immaterial whereas in a permutation, the ordering is essential.

Out of nine cells of a square, one cell is left blank and in the rest of the cells, numbers are written follow some rule. Get the rule and find out the proper option for the blank cell 

Identify the progression:

The numbers 1, 2, ..., 100 are arranged in the squares of an table in the following way: the numbers 1, ... , 10 are in the bottom row in increasing order,  numbers 11, ... ,20 are in the next row in increasing order, and so on. One can choose any number and two of its neighbors in two opposite directions (horizontal, vertical, or diagonal). Then either the number is increased by 2 and its neighbors are decreased by 1, or the number is decreased by 2 and its neighbors are increased by 1. After several such operations the table again contains all the numbers 1, 2, ... , 100. Prove that they are in the original order.

Unit digit in the number $$(12357)^{655}$$ is 

A tea party is arranged for $$16$$ people along two sides of a large table with $$8$$ chairs on each side. Four men to sit on one particular side and two on the other side. In how many ways can they be seated?