From a team of 6 students, in how many ways can we choose a captain and vice-captain assuming one person can not hold more than one position?

Evaluate the following

(i) 6 ! (ii) 5 ! – 2 !

How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter Exactly once?

How many words can be formed each of 2 vowels and 3 consonants from the letters of the given word – DAUGHTER?

It is needed to seat 5 boys and 4 girls in a row so that the girl gets the even places. How many are such arrangements possible?

Find the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

Find the number of 6 digit numbers that can be formed by using the digits 0, 1, 3, 5, 7, and 9. These digits shall be divisible by 10, and no digit shall be repeated?

Calculate how many numbers are there between 99 and 1000 having atleast one of their digits 7?

A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed?

Given that 5 flags are of different colours. Calculate how many different signals can be generated if each signal requires the use of 2 flags, one below the other?

Compute n!/ r!(n-r)!, when n=5 and r=2.