1. Probability - confusing question

I've been attempting this question (q14 part ii) for a while now, but I can't find a solution. The part where you have to have them in alphabetical order throws me off. Can someone help?

2. Re: Probability - confusing question

Originally Posted by MathWharf
I've been attempting this question (q14 part ii) for a while now, but I can't find a solution. The part where you have to have them in alphabetical order throws me off. Can someone help?

The number of three letters in alphabetical order is $_{26}\mathcal{C}_3=\binom{26}{3}=?$

3. Re: Probability - confusing question

How many different people could the club have whose first name starts with "A"? How many whose first name starts with "B"?

4. Re: Probability - confusing question

Does this take into account that none of the three letters are repeated? I'm nearly certain it does, but just in case..

5. Re: Probability - confusing question

The first letter has to be any letter between A and X (Y and Z would have repeats). The second letter could be anything from B to Y except for the first letter... This was my way of figuring it out but it made it more confusing than anything else.

6. Re: Probability - confusing question

Originally Posted by MathWharf
Does this take into account that none of the three letters are repeated? I'm nearly certain it does, but just in case..
Think about this. If you have as set of three letters (note that the language implies distinct letters) there is but one way to arrange them in alphabetical order. So we are just counting the subset of three from twenty-six.

7. Re: Probability - confusing question

I understand it now... I was thinking of a number of different possible combinations rather than number of members. So initials ZDA for example would have counted since it is part of the ADZ group. This page was also helpful: