In how many ways 6 children can be arranged in a line, such that

 two particular children of them are never together.

Assuming that any arrangement of letters forms a 'word', how many 'words' of any length can be formed from the letters of the word SQUARE?

Complete:

The number of ways to arrange the letters of the word CHEESE are__________.

A permutation lock will open if the right choice of 2 numbers (from 1 to 50) is selected. How many lock permutations can be made assuming no number is repeated?

Complete:

If ¹² P_r=1320, then r is equal to__________.

A special type of password consists of two different letters of the alphabet, where each letter is used only once. How many different possible passwords are there?

 A permutation lock will open if the right choice of 3 numbers (from 1 to 50) is selected. How many lock permutations can be made assuming no number is repeated?

How many numbers divisible by 5 and lying between 3000 and 4000 that can be formed from the digits 1, 2, 3, 4, 5, 6 (repetition of digits is not allowed)?

 In how many ways 6 children can be arranged in a line, such that

 two particular children of them are always together.

An encyclopedia has eight volumes. In how many ways can the eight volumes be replaced on the shelf?