Question 766577: The number of five digit telephone numbers having atleast one of their digits repeated is
a)900000 b)100000 c)30240 d)65760
Found 2 solutions by ramkikk66, narutowindy:
Answer by ramkikk66(644)   (Show Source):
You can put this solution on YOUR website!
Please check - doesn't look like any of the 4 choices is correct.
Here is the solution:
How many 5 digit telephone numbers are there in total?
From 10000 through 99999, there are 90000 of them.
Let us see - how many have all 5 digits different?
If all 5 have to be different,
1) The first digit can be filled in 9 ways (it cannot be 0)
2) Second can be filled in 9 ways (since 0 can be the second digit)
3) 3rd can be filled 8 ways, 4th in 7 ways and 5th in 6 ways. (Because we cannot reuse a digit)
So total number of 5 digit phone numbers with all the digits different is
9*9*8*7*6 = 27216.
Now, it is clear that all the other 5 digit phone numbers must have at least 1 digit repeating, since only 27216 of them have all the 5 digits as different!
So, the number of 5 digit phone numbers with at least 1 repeating digit = 90000 - 27216 = 62784.
:)
Answer by narutowindy(1) (Show Source):
You can put this solution on YOUR website! How many 5 digit telephone numbers are there in total?
From 10000 through 99999, there are 90000 of them.
Let us see - how many have all 5 digits different?
If all 5 have to be different,
1) The first digit can be filled in 9 ways (it cannot be 0)
2) Second can be filled in 9 ways (since 0 can be the second digit)
3) 3rd can be filled 8 ways, 4th in 7 ways and 5th in 6 ways. (Because we cannot reuse a digit)
So total number of 5 digit phone numbers with all the digits different is
9*9*8*7*6 = 27216.
Now, it is clear that all the other 5 digit phone numbers must have at least 1 digit repeating, since only 27216 of them have all the 5 digits as different!
So, the number of 5 digit phone numbers with at least 1 repeating digit = 90000 - 27216 = 65784.
:)
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