The total number of seven-digit numbers the sum of whose digits is even is

If all the words (with or without meaning) having five letters,formed using the letters of the word $SMALL$ and arranged as in a dictionary,then the position of the word $SMALL$ is:

Let $A$ be a set containing $10$ distinct elements. Then the total number of distinct functions from $A$ to $A$ is:

Let the eleven letters $A, B, \dots, K$ denote an arbitrary permutation of the integers $(1, 2, \dots, 11)$. Then, the product $(A - 1)(B - 2)(C - 3) \dots (K - 11)$ is:

How many permutations can be made by using all the letters of the word $MATHEMAGICA$?

From a group of $7$ men and $6$ women,five persons are to be selected to form a committee so that at least $3$ men are there on the committee. In how many ways can it be done?