# Homework Help: Probability quiz

1. Apr 18, 2013

### ParisSpart

In the expansion of ((x1 + x2 +.... + x33) ^ 4) how many monomials are of the form (xi ^ 2)*(xj^2)
with i not equal with j

if we add the coefficients of all these mononymon what is the sum?

E.g. the expansion of (x1 + x2 + x3) ^ 4 the requested number is 18

this is a probability quiz but i can think how to solve it with theory of probabilities any ideas for howmto beggin to solve this?

2. Apr 18, 2013

### Staff: Mentor

There is nothing probabilistic here, but combinatorics is important.
Have a closer look at your example - you should see some pattern about the coefficients. Find that pattern, and extend it to 33.

3. Apr 18, 2013

### haruspex

I don't think so. I believe 6x12x22 constitutes one monomial.

4. Apr 19, 2013

### Bacle2

I think it comes down to counting the number of ways of selecting a pair from {1,2,....,33}. For each

pair (xi[/SUBi,xj)) ,there will be one term xi[/SUP]2[/SUP]*xj2 . The general binomial coefficient ci in

ci x1y1x2y2x3y3 x4y4 counts

precisely the number of ways of selecting a total of y_1 x_1's, y_2 x_2's, etc. in the product.

Then ,for

xi2xj2, you're counting the number of ways of selecting exactly 2 x_i's and 2 x_j's from the expansion :

(x1+x2+x3+x4)...... ( 4 times )

How many ways can you choose a pair (xi,xj) from

(x1,x2, x3,...,x33)?

Last edited: Apr 19, 2013