Four Dice Are Rolled. The Number Of Possible Outcomes In Which Least One Die Shows 2 Is

If n > 1 and n divides (n – 1)! + 1, then 

In a group of 8 girls, two girls are sisters. The number of ways in which the girls can sit so that two sisters are not sitting together is

The number of words that can be formed by using the letters of the word MATHEMATICS that start as well as end with T is

The number of subsets of the set A = {a₁, a₂, … a_n} which contain even number of elements is

The number of ways in which we can post 5 letters in 10 letter boxes is

The number of five digit telephone numbers having at least one of their digits repeated is

Let P be a prime number such that P ≥ 23. Let n = p! + 1. The number of primes in the list n + 1, n + 2, n + 3, … n + p – 1 is

The term digit of 1! + 2! + 3! + … + 49! Is

A is a set containing n elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P. A subset Q of A is again chosen. The number of ways of choosing P and Q so that P ∩ Q = Ï• is