Thread: Help with combinatorics problem

Hi

I would appreciate if someone could explain how to solve the following problem:


"How many different five letter "words" can you write with the letters BILBANA"


The answer is 690 but I'm not entirely sure how to get there. I divide the problem into different cases:

A+B = 5!
A+A = 5!/2!
B+B = 5!/2!
A+B+B = ?
A+A+B = ?
A+A+B+B = ?



Thanks in advance

Hello Drdumbom

Originally Posted by Drdumbom

Hi

I would appreciate if someone could explain how to solve the following problem:


"How many different five letter "words" can you write with the letters BILBANA"


The answer is 690 but I'm not entirely sure how to get there. I divide the problem into different cases:

A+B = 5!
A+A = 5!/2!
B+B = 5!/2!
A+B+B = ?
A+A+B = ?
A+A+B+B = ?



Thanks in advance

You're right so far. Let me continue:

With A + B + B there will be two other letters chosen from the remaining 3. So we have two processes:

• Choose 2 out of 3 remaining letters. This can be done in ways.

• Arrange the 5 letters, which include a repeated B. This can be done in ways.

So A + B + B can be done in ways.

Similarly A + A + B can be done in ways.

And then in a similar way A + A + B + B + one other letter can be chosen and arranged in ways.

Therefore the total no of 'words' .

Grandad