probability

• Mar 22nd 2013, 03:56 PM
amyl95
probability
Mr and Mrs Zimmerman want to give their baby a name so that the baby's 3 initials are in alphabetical order.
how many different initials could the baby end up with? (for example B,G,Z is acceptable but G,B,Z is not etc.)

all i can think of is that there are 26 letters in the alphabet and 26 choose 3 = 2600, but how many of these groups of 3 letters are in alphabetical order?
• Mar 22nd 2013, 05:30 PM
Plato
Re: probability
Quote:

Originally Posted by amyl95
Mr and Mrs Zimmerman want to give their baby a name so that the baby's 3 initials are in alphabetical order. how many different initials could the baby end up with? (for example B,G,Z is acceptable but G,B,Z is not etc.)
all i can think of is that there are 26 letters in the alphabet and 26 choose 3 = 2600, but how many of these groups of 3 letters are in alphabetical order?

I suppose that we will follow the western world's custom and the Zimmerman's child will have the third initial, Z
But surely the child could be named Adan Abraham Zimmerman, AAZ.
You seem to assume the initials are different. WHY?
Why not Zeno Zerox Zimmerman, ZZZ?

There are $\binom{2+26-1}{2}$ ways to have an alpha string of length two in alphabetical order.