Melody

Thanks Alan, 

Alan's method is obviously the best way to so this problem.

Well if you know how to do it on the calculator and you wanted to know how to do it by hand you should have stated that in your question and not wasted people's time.

You should also have given the calculator answer so that people could easily see if their answer was correct.

Let's have a look at it again.

The first term is 1, you should automatically know that

The second term is 13 you should know that too.

You can work the rest out by hand but it is messy.

there are 14 terms in the entire Pascal triangle row.

You have half the row and it is symmetrical

If the sum of the entire row is 2^13 as you say (I did not know that - You could/should have mentioned this in your original question.

Then the sum of your terms is half that = 2^12

If I had read your last response properly I would know that you already worked this out. 

I wasted my own time it was not your fault this time.

Isn't it great when you work things out for yourself !

Good work!

Why did you get a point for that?

ok it is combination maths.

You can do it on your calculator.

13 nCr 0 + 13 nCr 1 + etc

Are they combination maths or vectors?

Yes, I have a pointer.

1 post = 1 question.

Yes, I already apologized.

I am also sorry if I caused you to waste your time with rechecking.

Thank you for showing us what you have attempted. 

That is what you should do EVERY time.

I for one cannot think straight with all those questions bombarding me.

One post is for one question.  I must have said that 1000 times.

But I will take a look at question 1

1) What is the probability that, in a roll of 3 fair dice, the same number is not rolled twice?

I listed out all the posssible combinations that could have happen with 1. I got 20. I multiplied that by 6 and got 120. Then I know that 6 cubed is 216... so the I thought the probability must be 120/216 = 15/27.

You listed all the possibilities .....  Where is your list?  Do you mean a list where one only happens once?

one of your combinations would be 1,2,3,

Now  if you do the same thing for the number 2 and add them together then this combination will appear again.

Hence I expect you have double counted. 

See I can teach you if you show me where you are at!  Well maybe anyway.

With 3 rolls there is a 6^3 = 216 possible combination,

111       1 way

112        3ways

113         3ways

114         3ways

115         3ways

116         3ways

So that is 16 ways     (maybe that is what you did and one of us counted wrong?)

the same would  be for the one 5 numbers so

16*6= 96

so that appears to be   96/216 = 4/9

Edit:

This is the probability that a number will repeat.

The probability that a number will not repeat is 1-4/9 = 5/9

Now the idea is that if possible you see if my answer is correct.

(If you know what the answer should be your should already have told us)

If the answer is wrong then you politely and clearly explain why you think this. 

(eg I put the answer in the answer box and the computer said it was wrong)

If the answer is correct then you try to see what I have done right and what you did wrong.

If you have questions then you ask for further explanation.

After you have digested all this and learned all that you can learn,

Then

You attempt the next question again by yourself and if you can not do it you present the next question and what you have tried in a completely new post. 

-----------------------------------------------

Now digest all I have told you .

You could start by deleting questions 2 to 6 from this post.

One post = one question.

Sorry Guest, I had contradicted you but I need to look again.   

All five digits are different



The digit in the ten thousands place is greater than 7         so it is 8 or 9 

The sum of all five digits is 18,                                     others add to 10 or 9                                 

The greatest digit is equal to the sum of the other four digits.     So the the biggest is 9 and the others add to 9

None of the five digits are 1                                                0+2+3+4=9

so the digits from biggest to smallest are   9,4,3,2,0

The biggest possible number is   94 320    just like guest said.