How To Evaluate Binomial Coefficients: Definition and Examples
Learn how to evaluate binomial coefficients by understanding the formula n above r = n! / (r! * (n-r)!) with examples and restrictions on values of n and r. Get insights on the definition and application of binomial coefficients in mathematics.
Video Summary & Chapters
No chapters for this video generated yet.
Video Transcript
in this video we're going to talk about
how to evaluate the binomial coefficient
so let's go over the definition for it
this expression
which means n above r
this is equal to n factorial
over
R factorial
times n minus r factorial
where N is a number equal to or greater
than r
n can't be less than R if R is 4 n could
be 4 5 6
or some other non-negative integer above
that
so now let's work on some examples
let's say we have this expression
8 above 3.
go ahead and evaluate that
so using the formula we can see that n
is eight
and r
a string
and then we have n minus r so that's 8
minus 3.
now how do we evaluate a factorial
expression
if you saw this 4 factorial what does
that mean 4 factorial is equivalent to
this expression it's 4 times 3 times 2
times 1.
so 4 times 3 is 12 times 2 is 24 times 1
that's going to be 24.
3 factorial is simply three times two
times one which is 6.
zero factorial
is one and one factorial is also one so
those are some things that you just need
to commit to memorization zero and one
factorial
so knowing that we can evaluate this
expression
so we have 8 factorial over three
factorial and then eight minus three
that's going to be five
so we have 5 factorial
now a factorial is eight times seven
times six
times five factorial because this will
take us all the way to 1. but we don't