1. ## permutation

How many 4-digit numbers with values 6000 and above can be formed from the digits 4,5,6,7,8, where every digit cannot be used more than once in a number? Among the numbers formed, how many are odd number?

I've got 3 X 4 X 3 X 2 =72, but I still can't answer the second question..

2. ## Re: permutation

Originally Posted by Trefoil2727
How many 4-digit numbers with values 6000 and above can be formed from the digits 4,5,6,7,8, where every digit cannot be used more than once in a number? Among the numbers formed, how many are odd number?
I've got 3 X 4 X 3 X 2 =72, but I still can't answer the second question..
There are $(3)(3)(2)(1)$ of those numbers end in $5$.

There are $(2)(3)(2)(1)$ of those numbers end in $7$.

So what is the answer to the second question?

3. ## Re: permutation

Originally Posted by Plato
There are $(3)(3)(2)(1)$ of those numbers end in $5$.

There are $(2)(3)(2)(1)$ of those numbers end in $7$.

So what is the answer to the second question?
12, how did you get that?

4. ## Re: permutation

Originally Posted by Trefoil2727
12, how did you get that?
Any of the four digit numbers described in the question must end in 5 or 7 to be odd.

5. ## Re: permutation

Originally Posted by Trefoil2727
How many 4-digit numbers with values 6000 and above ... I've got 3 X 4 X 3 X 2 =72,
Did you mean to say 60,000 and above? If so, your answer is correct. But if in fact the question asks about numbers 6000 and above then any combination of all 5 digits will do it, plus any 4-digit number that starts with 6, 7, or 8.

6. ## Re: permutation

Originally Posted by ebaines
Did you mean to say 60,000 and above? If so, your answer is correct. But if in fact the question asks about numbers 6000 and above then any combination of all 5 digits will do it, plus any 4-digit number that starts with 6, 7, or 8.
The OP says 4-digit numbers,

Originally Posted by Trefoil2727
How many 4-digit numbers with values 6000 and above can be formed from the digits 4,5,6,7,8, where every digit cannot be used more than once in a number?

7. ## Re: permutation

Originally Posted by Plato
The OP says 4-digit numbers,
Ah! I should have read the original post moire carefully. Thanks.

8. ## Re: permutation

Originally Posted by Plato
Any of the four digit numbers described in the question must end in 5 or 7 to be odd.
can I use (3)(2)(1)(2)? I count 5 and 7 together

9. ## Re: permutation

Originally Posted by Trefoil2727
can I use (3)(2)(1)(2)? I count 5 and 7 together
No you cannot. If the number ends 5 you can still have three choices for the first digit.

However, if the number ends 7 you have only two choices for the first digit.