SOLUTION: 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? B. If repetition of the digits is not p

Question 1191410: 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?
B. If repetition of the digits is not permitted?
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!
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

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