Permutations and Combinations · Mathematics · KCET

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

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

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?

$$A$$ 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

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

The value of $${ }^{16} C_9+{ }^{16} C_{10}-{ }^{16} C_6-{ }^{16} C_7$$ 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

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