# How many 7 digit inters there using only the digits 2,3,4,5,6,7,8

• Dec 14th 2011, 10:58 AM
ehpoc
How many 7 digit inters there using only the digits 2,3,4,5,6,7,8
How many EVEN 7 digit inters there using only the digits 2,3,4,5,6,7,8? EDIT: forgot to add the word even.

I thought this was easy, but when I got my assignment back it was wrong.

For my answer I put 4*6!

4 ways to put either 2,4,6,8 in the last position multiplied by 6! as the ways we can arrange the rest of the numbers.

If this is incorrect.....what am i missing?

edit: I also got zero on a similar question.

In a class of 19 children, with 11 boys and 8 girls - how many ways can we choose a team of 10 children containing at least 5 boys?

I put...

(11c5) to select the boys. Multiplied by (14c5) to select the rest of the 5 students.

The correct solution apparently is (11c5)(8c5)+(11c6)(8c4)+(11c7)(8c3)+(11c8)(8c2)+(1 1c9)(8c1)+(11c10)(8c0)
• Dec 14th 2011, 11:04 AM
Plato
Re: How many 7 digit inters there using only the digits 2,3,4,5,6,7,8
Quote:

Originally Posted by ehpoc
How many 7 digit inters there using only the digits 2,3,4,5,6,7,8?
I thought this was easy, but when I got my assignment back it was wrong.
For my answer I put 4*6!
4 ways to put either 2,4,6,8 in the last position multiplied by 6! as the ways we can arrange the rest of the numbers. If this is incorrect.....what am i missing?

2,323,265 is a seven digit integer using only those seven digits.
The question did not say that digits could be repeated. Did it?
• Dec 14th 2011, 11:20 AM
ehpoc
Re: How many 7 digit inters there using only the digits 2,3,4,5,6,7,8
So in this case it would be 4*7^6?
• Dec 14th 2011, 12:04 PM
Plato
Re: How many 7 digit inters there using only the digits 2,3,4,5,6,7,8
Quote:

Originally Posted by ehpoc
So in this case it would be 4*7^6?

The question you posted said nothing about the number being even.
Did you leave that out? If not why are you using that 4?
• Dec 14th 2011, 12:26 PM
ehpoc
Re: How many 7 digit inters there using only the digits 2,3,4,5,6,7,8
Yes so sorry! I left out the word even.

So my rational is that there are 4 unique evens to select from multiplied by 7^6 for the other six numbers.

Correct?
• Dec 14th 2011, 12:32 PM
Plato
Re: How many 7 digit inters there using only the digits 2,3,4,5,6,7,8
Quote:

Originally Posted by ehpoc
Yes so sorry! I left out the word even.
So my rational is that there are 4 unique evens to select from multiplied by 7^6 for the other six numbers. Correct?