Wednesday

July 23, 2014

July 23, 2014

Posted by **Joe** on Monday, May 23, 2011 at 9:27pm.

- Math -
**MathMate**, Tuesday, May 24, 2011 at 9:10amThe number of terms in a multinomial expansion of m terms raised to the nth power is equal to C(n+m-1,n).

In the present case,

n=5, m=3, so

C(n+m-1,n)=C(5+3-1,5)=C(7,5)=7*6/(2*1)=21

In the same vein, you may be interested to know that the individual coefficients for the terms

a^p*b^q*c^r (where p+q+r=n)

is

C(n,p,q,r)

=n!/(p!q!r!)

For example, the term a²b²c

has p=2,q=2,r=1

so the coefficient is

C(5,2,2,1)

=5!/(2!2!1!)

For more interesting facts, see:

http://en.wikipedia.org/wiki/Multinomial_theorem

**Related Questions**

Math - How many terms are in the expansion of (a+b+c)^3 after like terms have ...

Managerial Economics - What would it mean if an expansion path eventually had a ...

Math - 1. The question is: List the like terms in the following group of terms. ...

MATH STUCK:-( - I am having some difficulties factoring polynomials and I use ...

math - when you are multiplying an equation how do you find like terms The ones ...

Pre-Calculus - Need help with this question, dont get it. Given the relation x^2...

Pre-Calculus Graphs expansions/compressions - Need help with this question, dont...

math - Can anyone help with combining like terms? The question - 11 + 5t^2 + t...

english/poetry - What poet/songwriter wrote these words? Like a bird on the wire...

Math - Hi everyone, I would like some help with Math.. And I would like help ...