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  7. How To Evaluate Binomial Coefficients: Definition and Examples

How To Evaluate Binomial Coefficients: Definition and Examples

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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.
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Video Transcript

0:01
in this video we're going to talk about
0:03
how to evaluate the binomial coefficient
0:07
so let's go over the definition for it
0:11
this expression
0:13
which means n above r
0:17
this is equal to n factorial
0:20
over
0:22
R factorial
0:24
times n minus r factorial
0:28
where N is a number equal to or greater
0:31
than r
0:32
n can't be less than R if R is 4 n could
0:37
be 4 5 6
0:39
or some other non-negative integer above
0:43
that
0:47
so now let's work on some examples
0:53
let's say we have this expression
0:57
8 above 3.
1:00
go ahead and evaluate that
1:02
so using the formula we can see that n
1:05
is eight
1:06
and r
1:08
a string
1:10
and then we have n minus r so that's 8
1:14
minus 3.
1:17
now how do we evaluate a factorial
1:20
expression
1:24
if you saw this 4 factorial what does
1:26
that mean 4 factorial is equivalent to
1:29
this expression it's 4 times 3 times 2
1:32
times 1.
1:34
so 4 times 3 is 12 times 2 is 24 times 1
1:39
that's going to be 24.
1:42
3 factorial is simply three times two
1:45
times one which is 6.
1:49
zero factorial
1:51
is one and one factorial is also one so
1:55
those are some things that you just need
1:57
to commit to memorization zero and one
1:59
factorial
2:03
so knowing that we can evaluate this
2:05
expression
2:08
so we have 8 factorial over three
2:11
factorial and then eight minus three
2:13
that's going to be five
2:15
so we have 5 factorial
2:18
now a factorial is eight times seven
2:22
times six
2:24
times five factorial because this will
2:27
take us all the way to 1. but we don't
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