Question 883540: Hello there, I need some help with my homework :) the question is
How many 4 digit numbers may be formed that are greater than 3,255 from the numbers, 2,3,4,5 and 6, if repetition is allowed?
My first answer was 410 but then I tried to do it again and the result was 406.. I might be right and I might be wrong and I just wanted to make sure please help thank you so much and have a great day:)
Found 2 solutions by rothauserc, KMST:
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! The first digit can be any one of (3, 4, 5, 6) since it can not be 2
The second digit can be any one of (2, 3, 4, 5, 6)
The third digit can be any one of (5, 6) if the second digit is a 2
The third digit can be any one of (2, 3, 4, 5, 6) if second digit is not a 2
The fourth digit can be a (6) if the second digit is a two and third digit is a 5
The fourth digit can be a (2, 3, 4, 5, 6) if the second digit is a two and third digit is a 6
The fourth digit can be one of (2, 3, 4, 5, 6) if the second digit is not a 2
Therefore we have
4 * 5 * 5 * 5 - (3 * 4 * 5) = 440
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! I get a different number.
I checked by figuring it different ways, but I might be missing something.
If you use 4, 5, or 6 as the first digit, your number will surely be greater than 3,255.
The first digit cannot be 2, and that greatly limits the choices.
Choosing 3 as the first digit limits your choices for the other digits, because
3,222, 3,223, 3,224, 3,225, 3,226,
3,232, 3,233, 3,234, 3,235, 3,236,
3,242, 3,243, 3,244, 3,245, 3,246,
3,252, 3,523, 3,254, and 3,255 are not greater than 3,255,
so you have  less choices.
Other than the limitations above,
you have 5 choices (2, 3, 4, 5, or 6) for each digit.
That gives you  choices for the last 3 digits.
Using 3, 4, 5, or 6 as a first digit (4 choices),
combined with those  choices for the last 3 digits gives you
 numbers that
use only 2, 3, 4, 5, and 6 as digits, with 3, 4, 5, or 6 as first digit.
If we subtract from those  numbers
the that start with 3 and are not greater than 3,255,
we get  .
NOTE: Listing the numbers is not a good way to count them.
I tried listing the numbers that started with 3,
and my count did not add up, because I was missing some numbers.
I know I make lots of distracted mistakes, so I always try to check my results.
I check using different ways, because when figuring things the same way, I usually make the same mistake.
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