How many 4-letter words can be formed from DESTINY? (NOTE:The
word may not mean anything.)
A. If repetition of the digits is permitted?
Choose the 1st letter any of 7 ways.
There are still 7 ways to choose the 2nd letter, since you can repeat the
letter you chose first.
Choose the 2nd letter any of 7 ways.
There are still 7 ways to choose the 3rd letter, since you can repeat the
letters you chose first and second.
Choose the 3rd letter any of 7 ways.
There are still 7 ways to choose the 4th letter, since you can repeat the
letters you chose first, second, and third.
Choose the 4th letter any of 7 ways.
7x7x7x7 = 74 = 2401
B. If repetition of the digits is not permitted?Choose the 1st letter any of 7 ways.
There are only 6 ways to choose the 2nd letter, since you cannot repeat
the letter chosen first.
Choose the 2nd letter any of 6 ways.
There are only 5 ways to choose the 3rd letter, since you cannot repeat
the letters chosen first or second.
Choose the 3rd letter any of 5 ways.
There are only 4 ways to choose the 4th letter, since you cannot repeat
the letters chosen first, second or third.
Choose the 4th letter any of 4 ways.
7x6x5x4 = 840.
Edwin
