find the binomial coefficient of 5th term of (a+b)8?
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Step-by-step explanation:
The fifth term is the middle term of nine, with coefficient given by all the ways of choosing
4
items out of
8
, namely the ways of choosing
4
a
's out of
8
binomial factors.
(
8
4
)
a
4
b
4
=
8
!
4
!
4
!
a
4
b
4
=
8
×
7
×
6
×
5
4
×
3
×
2
×
1
a
4
b
4
=
1680
24
a
4
b
4
=
70
a
4
b
4
The coefficient
(
8
4
)
=
70
can be picked out as the middle term of the row of Pascal's triangle that begins
1
,
8
,
...
:
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