Simple Math ??????????

[jrs1947]

Not for this country boy, so I have come to you Math experts for the solution to a math problem, and that is.
How many differnt combinations could I get using any 3 letters and any 3 single digit numbers ?
Some friends and I were talking about the numerous possibilities using just 3 letters and 3 single digit numbers to see how many cattle that would brand.
Best Regards ..............jstout

 

[jrs1947]

Yes you can mix letters and numbers at will and yes zero is a number as well as O being a letter,I obviously dont know how to do the math but Im told by the state of Texas the correct answer is 17,576,000 what i am wondering is how they came to the answer of 17,576,000 ? and if that is correct ?
Thanks...............jstout

 

[pka]

Yes you can mix letters and numbers at will and yes zero is a number as well as O being a letter,I obviously dont know how to do the math but Im told by the state of Texas the correct answer is 17,576,000 what i am wondering is how they came to the answer of 17,576,000 ? and if that is correct ?

Here is what Texas did: \(\displaystyle 26^3\cdot 10^3=17,576,000\).
That is, each brand contains three letters and three digits in any order.

 

[jrs1947]

Would you be so kind as to provide some detail so that a country boy can comprehend the process ?
thanks.................jstout

 

[jrs1947]

Jeff, you provided a detailed answer, sorry I did not pose the question well, can you work out the correct answer for me ?

I thought your explanation was exellent...................thanks again
jstout

 

[jrs1947]

Anyone ?? care to provide the steps required to arrive at the answer 17,576,000 ?
thanks again

 

[pka]

Think of six spaces: \(\displaystyle \_\_~\_\_~\_\_~\_\_~\_\_~\_\_\)
Pick any three for a letter and the other three are for digits.
There are \(\displaystyle 26^3\) ways to choose three letters and \(\displaystyle 10^3\) ways choose the digits.

 

[jrs1947]

I hate to show my ignorance pka, but would you please explain the formula, I dont have a way to post your 26 and 10 number, explanation, but that is the part an ole cowboy dont get.
thanks again, I guess what i am really asking is why are you taking 26 and 10 to the 3rd power ?
thanks again.

 

[jrs1947]

thanks men, i got it now, and i sure appreciate it.......................good luck
jstout

 

[pka]

I disagree with pka. I do disagree, however, with pka and Texas.

The original questions says COMBINATIONS.

Not for this country boy, so I have come to you Math experts for the solution to a math problem, and that is.
How many different combinations could I get using any 3 letters and any 3 single digit numbers ?

There is a simple way to calculate the first step, but it is not intuitive. So bear with me while I go about this the long way. So I am bigger than Texas. I get \(\displaystyle 20 * 26 * 26 * 26 * 10 *10 *10 = 351,520,000 \)

If you want to look mathematical that is \(\displaystyle \dbinom{6}{3} * 26^3 * 10^3 = 351,520,000\)

If order makes a difference, this is correct

 

[jrs1947]

Order does not make a differnce.................thanks again & good luck

 

[pka]

Order does not make a difference

Like I said, the OP used the word combinations. Mathematics is a word game. To any mathematician the word combination implies content and not order.

 

[afrazer721]

Not for this country boy, so I have come to you Math experts for the solution to a math problem, and that is.
How many differnt combinations could I get using any 3 letters and any 3 single digit numbers ?
Some friends and I were talking about the numerous possibilities using just 3 letters and 3 single digit numbers to see how many cattle that would brand.
Best Regards ..............jstout

I used the combinations formula since order doesn't matter.
Combination of k things from n things is nCk=n!/(n-k)!k!.
So, 26C3 * 10C3=(26!/(26-3)!3!)(10!/(10-3)!3!)=the # of cattle that can be branded.
Hope this help out.

"I really don't think about the I-could-have-beens. Life is only about the I-tried-to-do. I don't mind the
failure, but I can't imagine that I'd forgive myself if I didn't try." Nikki Giovanni, poet

 

[pka]

I used the combinations formula since order doesn't matter. Combination of k things from n things is nCk=n!/(n-k)!k!.
So, 26C3 * 10C3=(26!/(26-3)!3!)(10!/(10-3)!3!)=the # of cattle that can be branded.

@afrazer721,Do you bother to read the entire thread before posting a reply? This is the third that you have posted a completely incorrect answer.
The answer above requires that the letters and the digits are all distinct. That is not the case.
Please in the future, make sure that you read all replies before post so that you have a full grasp of the thread.