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<pre>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) = 5<sup>5</sup> = 3125 ways.</pre>(2) The number must be odd and repetitions are not allowed<pre>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.</pre>(3) the number must be greater than 30,000 and repetition is not allowed.<pre>
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</pre>