Permutations And Combinations - Algebra - Mathematics Previous Year Questions

If \(P(n): 2^n< n !\) Then the smallest positive integer for which \(P(n)\) is true, is

The number of 4 digit numbers without repetition that can be formed using the digits \(1,2,3,4,5,6,7\) in which each number has two odd digits and two even digits is

The value of \({ }^{16} C_9+{ }^{16} C_{10}-{ }^{16} C_6-{ }^{16} C_7\) is

A student has to answer 10 questions, choosing at least 4 from each of the parts \(A\) and \(B\). If there are 6 questions in part \(A\) and 7 in part \(B\), then the number of ways can the student choose 10 questions is

\(A\) and \(B\) are non-singleton sets and \(n(A \times B)=35\). If \(B \subset A\), then \({ }^{n(A)} C_{n(B)}\) is equal to

If all permutations of the letters of the word MASK are arranged in the order as in dictionary with or without meaning, which one of the following is 19th word?

Ten chairs are numbered as 1 to 10. Three women and two men wish to occupy one chair each. First the women choose the chairs marked 1 to 6 , then the men choose the chairs from the remaining. The number of possible ways is

$$\text { The number of diagonals that can be drawn in an octagon is }$$