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Byju's Answer
Standard XII
Mathematics
Permutation: n Different Things Taken All at a Time When All Are Not Different.
Find the numb...
Question
Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements do all vowels occur together.
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Solution
I
N
D
E
P
E
N
D
E
N
C
E
Arranging
5
vowels
Since vowels are coming together
they can be
E
E
E
E
I
,
I
E
E
E
E
, and So on
In
I
E
E
E
E
there are
4
E
since letter are repeating total arrangement
=
5
!
4
!
Arranging Remaining
no we need to arrange
7
+
1
=
8
Hence are
3
N
,
2
D
We use
=
8
!
3
!
2
!
Required No.
=
5
!
4
!
×
8
!
3
!
2
!
=
(
8
×
7
×
6
×
5
×
4
)
(
5
×
4
!
)
4
!
×
3
!
×
2
=
16
,
800
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Permutation: n Different Things Taken All at a Time When All Are Not Different.
Standard XII Mathematics
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