SOLUTION: Premutations 1. How many numbers consisting of five digits each can be made from the digits 1,2,3,.......,9 if (a)the numbers must be odd (b) the first two digits of each number a

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Question 841541: Premutations
1. How many numbers consisting of five digits each can be made from the digits 1,2,3,.......,9 if (a)the numbers must be odd (b) the first two digits of each number are even. [ans: (a) 8400 (b) 2520]
2. Solve the proceeding problem if repetitions of digits are allowed.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
(a)the numbers must be odd
Always choose the most restrictive digit first.

Choose the last digit any of these: 1,3,5,7,9.  That's 5 ways.
Choose the first digit any of the 8 remaining ways.
Choose the second digit any of the 7 remaining ways.
Choose the third digit any of the 6 remaining ways.
Choose the fourth digit any of the 5 remaining ways.

Answer = 5򊤋򉼱 = 8400 

2. Solve the proceeding problem if repetitions of digits are allowed. 

Always choose the most restrictive digit first.

Choose the last digit any of these: 1,3,5,7,9.  That's 5 ways.
Choose the first digit any of the 9 ways.
Choose the second digit any of the 9 ways.
Choose the third digit any of the 9 ways.
Choose the fourth digit any of the 9 ways.

Answer = 5򊷹򊷹 = 32805

Edwin