SOLUTION: How many different 5 digit numbers can be formed from the digit 1,2,3,4 and 5 if (i). There are no restrictions on the digit and repetitions are allowed. (ii). The number is odd

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Question 1114331: How many different 5 digit numbers can be formed from the digit 1,2,3,4 and 5 if
(i). There are no restrictions on the digit and repetitions are allowed.
(ii). The number is odd and no repetition is allowed.
(iii).The number is even and reputation are allowed.
(iv). The number is greater than 50,000 and no repetitions are allowed.
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
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.
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 = 55 = 3125 ways
(ii). The number is odd and no repetitions are allowed.
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
(iii).The number is even and reputations are allowed.
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 = 2×54 = 1250 ways
(iv). The number is greater than 50 000 and no repetitions are allowed
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
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