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Byju's Answer
Standard VIII
Mathematics
Number of Ways of Selecting "k" Things Out of "n" Things at a Time
In how many w...
Question
In how many ways can a student choose 6 courses out of 10 courses?
A
5040
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B
210
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C
6
!
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D
6
!
3
!
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Solution
The correct option is
B
210
We know that number of ways of selecting "r" things out of "n" things at a time is equal to
n
C
r
=
n
!
(
n
−
r
)
!
×
r
!
.
According to question student have to select
6
courses out of
10
courses.
Number of ways of doing that is
10
C
6
=
10
!
(
10
−
6
)
!
×
6
!
=
10
!
4
!
×
6
!
⇒
10
C
6
=
10
×
9
×
8
×
7
×
6
!
24
×
6
!
=
5040
24
=
210
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