Question 1114331
How many different 5 digit numbers can be formed 
from the digit 1,2,3,4 and 5 if 

(i). They are no restrictions on the digit and repetitions are allowed.<pre>Choose the 1st digit 5 ways.
Choose the 2nd digit 5 ways.
Choose the 3rd digit 5 ways.
Choose the 4th digit 5 ways.
Choose the 5th digit 5 ways.

5×5×5×5×5 = 5<sup>5</sup> = 3125 ways</pre>(ii). The number is odd and no repetitions are allowed.<pre>Choose the 5th digit 3 ways.  (either 1,3, or 5)
Choose the 1st digit 4 ways.
Choose the 2nd digit 3 ways.
Choose the 3rd digit 2 ways.
Choose the 4th digit 1 way.

3×4×3×2×1 = 72 ways</pre>(iii).The number is even and reputations are allowed.<pre>Choose the 5th digit 2 ways.  (either 2 or 4)
Choose the 1st digit 5 ways.
Choose the 2nd digit 5 ways.
Choose the 3rd digit 5 ways.
Choose the 4th digit 5 ways.

2×5×5×5×5 = 2×5<sup>4</sup> = 1250 ways</pre>(iv). The number is greater than 50 000 and no repetitions are allowed<pre>Choose the 1st digit 1 way. (as 5)
Choose the 2nd digit 4 ways.
Choose the 3rd digit 3 ways.
Choose the 4th digit 2 ways.
Choose the 5th digit 1 way.

1×4×3×2×1 = 60 ways

Edwin</pre>