SOLUTION: The digits 1,2,3,4, and 5 are to be used to form five-digit numbers. How many different number can be formed if (1).repetitions are permitted (2) The number must be odd and repetit

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Question 1069247: The digits 1,2,3,4, and 5 are to be used to form five-digit numbers. How many different number can be formed if (1).repetitions are permitted (2) The number must be odd and repetitions are not allowed (3) the number must be greater than 30,000 and repetition is not allowed.
Found 2 solutions by Edwin McCravy, trsomas23@gmail.com:
Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
The digits 1,2,3,4, and 5 are to be used to form five-digit numbers.
How many different number can be formed if
(1).repetitions are permitted
Choose the first digit any of the 5 ways.
Choose the second digit any of the 5 ways.
Choose the third digit any of the 5 ways.
Choose the fourth digit any of the 5 ways.
Choose the fifth digit any of the 5 ways.

Answer (5)(5)(5)(5)(5) = 55 = 3125 ways.
(2) The number must be odd and repetitions are not allowed
Choose the fifth digit any of these 3 ways:  1, 3 or 5.
Choose the first digit any of the remaining 4 ways.
Choose the second digit any of the remaining 3 ways.
Choose the third digit either of the remaining 2 ways.
Choose the fourth digit the only remaining 1 way.

Answer (3)(4)(3)(2)(1) = 72 ways.
(3) the number must be greater than 30,000 and repetition is not allowed.
Choose the first digit any of these 3 ways:  3, 4, or 5.
Choose the second digit any of the remaining 4 ways.
Choose the third digit any of the remaining 3 ways.
Choose the fourth digit either of the remaining 2 ways.
Choose the fifth digit the only remaining 1 way.

Answer (3)(4)(3)(2)(1) = 72 ways.

Edwin
Answer by trsomas23@gmail.com(17)   (Show Source): You can put this solution on YOUR website!
1) = 3125
2) The unit digit should be 1, 3, 5
No. of ways to fill the unit digit = 3
No. of ways to fill the remaining 4 places = 4! = 24
3 x 24 = 72
3) Leftmost digit should be 3, 4 or 5
No. of ways to fill the leftmost digit = 3
No. of ways to fill the remaining 4 places = 4! = 24
3 x 24 = 72
Email: trsomas23@gmail.com
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