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October 23, 2016
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