How many ways can a king, a knight, and a rook be placed on a chessboard?
A chessboard has 64 squares.
There are 64 ways to place the king on the board.
After the king is placed, there are 63 squares remaining to place the knight.
After the knight is on the board, there are 62 choices left for the rook.
Altogether there are 64 times 63 times 62 ways to place the three different pieces on the board.
(64)(63)(62)=249984.
How many different ways are there to create 5 letter words if each letter can only be used once?
There are 26 letters in the English alphabet.
There are 26 ways to choose the first letter.
After the first letter is placed, there are 25 ways to choose the second letter.
After the second letter is placed, there are 24 ways to choose the third letter.
After the third letter is placed, there are 23 ways to choose the fourth letter.
After the fourth letter is placed, there are 22 ways to choose the fifth letter.
Altogether there are 26 times 25 times 24 times 23 times 22 ways to create 5 letter words without using any letters more than once.
(26)(25)(24)(23)(22)=7893600.
How many different 4 digit numbers can be created using all the following digits: 3,4,7,9?
The first digit may appear in one of 4 places.
After the first digit is placed, there are 3 ways to place the second digit.
After the second digit is placed, there are 2 ways to place the third digit.
After the third digit is placed, there is 1 ways to place the fourth digit.
Altogether there are 4 times 3 times 2 times 1 ways of creating a 4 digit number using all the digits: 3,4,7,9.
(4)(3)(2)(1)=24.
