How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if

There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of:

Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:

There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find :

Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find