# Thread: Stumped on two questions

1. ## Stumped on two questions

Hey all. I am currently trying to work through a couple of probability problems and i am just completely stumped.

1. How large must the alphabet be in order that 1 million people can be identified by three letter initials.

2. There are three kinds of shirts on sale. If two shirts are sold, how many possibilities are there.

Any insight is much apprecitaed. Thank you

2. Hello, multivariablecalc!

1. How large must the alphabet be in order that 1 million people
can be identified by three letter initials?

Let $\displaystyle x$ = number of letters in the alphabet.

Then there are: .$\displaystyle x^3$ possible 3-letter initials.

We want: .$\displaystyle x^3 \:\geq \:1,\!000,\!000 \quad\Rightarrow\quad x \:\geq \:100$

Therefore, there must be at least 100 letters in the alphabet.

2. There are three kinds of shirts on sale.
If two shirts are sold, how many possibilities are there?

There are 3 choices for the first sale.
There are 3 choices for the second sale.

Therefore, there are: .$\displaystyle 3 \times 3 \:=\:9$ possibilities.

3. soroban thanks so much for your response and taking the time.