permutations
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I guess he means that you can only use each digit once, if not, the answer is infinite.
To be odd, the number has to end on 3, 5 or 7.
To be bigger than 500000, the number has to start with 5, 6 or 7.
So this are the possibilities:
the number can start with 3, and end on 5 or 7
the number can start with 5, and end on 3 or 7
the number can start with 7, and end on 3 or 5.
this are 6 possibilities.
the rest of the digits don't matter.
so the total amount of odd numbers over 500000 with those digits is 6 * Permutations(4) = 6 * 4! = 144
To be odd, the number has to end on 3, 5 or 7.
To be bigger than 500000, the number has to start with 5, 6 or 7.
So this are the possibilities:
the number can start with 3, and end on 5 or 7
the number can start with 5, and end on 3 or 7
the number can start with 7, and end on 3 or 5.
this are 6 possibilities.
the rest of the digits don't matter.
so the total amount of odd numbers over 500000 with those digits is 6 * Permutations(4) = 6 * 4! = 144
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There are 6 digits: 2,3,4,5,6,7
If we can repeat the digits, then there will be infinite numbers greater than 500000.
If we are not allowed to repeat any of the digits, then check the following.
As the number has to be greater than 500000, it should start with either 5, 6 or 7, we shall count separately.
Starting with 5:-
The number has to be odd, so there are 2 choices for one's position (namely 3 or 7).
The other 4 positions can be filled by the 4 digits in 4! ways.
So the total of numbers that can be made is 2 x 4! = 2 x 24 = 48.
Starting with 6:-
As the number has to be odd, there are 3 choices for one's position (namely 3, 5 or 7).
The other 4 positions can be filled by 4 digits in 4! ways.
So the total of numbers that can be made is 3 x 4! = 3 x 24 = 72.
Starting with 7:-
This is similar to starting with 5. And the total of numbers that can be made is 48.
So the all total of numbers that can be made is 48 + 72 + 48 = 168.
If we can repeat the digits, then there will be infinite numbers greater than 500000.
If we are not allowed to repeat any of the digits, then check the following.
As the number has to be greater than 500000, it should start with either 5, 6 or 7, we shall count separately.
Starting with 5:-
The number has to be odd, so there are 2 choices for one's position (namely 3 or 7).
The other 4 positions can be filled by the 4 digits in 4! ways.
So the total of numbers that can be made is 2 x 4! = 2 x 24 = 48.
Starting with 6:-
As the number has to be odd, there are 3 choices for one's position (namely 3, 5 or 7).
The other 4 positions can be filled by 4 digits in 4! ways.
So the total of numbers that can be made is 3 x 4! = 3 x 24 = 72.
Starting with 7:-
This is similar to starting with 5. And the total of numbers that can be made is 48.
So the all total of numbers that can be made is 48 + 72 + 48 = 168.
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did you mean,
How many 6 digit odd numbers can be made from 2, 3, 4, 5, 6, 7 that are greater than 500,000 using the digits just once?
starts with 5, has to end in 7, or 3
1 * 4 * 3 * 2 * 1 * 2 = 48 different numbers that start with 5
starts with 6, has to end in 3, 5, 7
1 * 4 * 3 * 2 * 1 * 3 = 72
starts with 7, has to end in 3, 5
1 * 4 * 3 * 2 * 1 * 2 = 48
48 + 72 + 48 = 168
How many 6 digit odd numbers can be made from 2, 3, 4, 5, 6, 7 that are greater than 500,000 using the digits just once?
starts with 5, has to end in 7, or 3
1 * 4 * 3 * 2 * 1 * 2 = 48 different numbers that start with 5
starts with 6, has to end in 3, 5, 7
1 * 4 * 3 * 2 * 1 * 3 = 72
starts with 7, has to end in 3, 5
1 * 4 * 3 * 2 * 1 * 2 = 48
48 + 72 + 48 = 168
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An unlimited amount, there is no limit to high high one can count and thus there are an unlimited amount of possibilities for them.
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3x5x4x3x2x1 = 360
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infinite
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An infinite number. Did you ask what you really meant to?