find the number of different arrangements of the letters of the word"OGBOMOSO"
Answers
Answer:
Answer
There are 5 vowels in the given word I,N,D,E,P,E,N,D,E,N,C,E
4E
′
s and I
′
s
They have occur together we treat them as single object
We treat
EEEEI
as a single object.
So our letters become
EEEEI
N
D
,
P
N
D
N
C
We arrange them now
Arranging 5 vowels:
Since vowels are coming together, they can be
EEEEI
IEEEE
EEIEE
and so on.
In EEEEI there are 4E
Since letter are repeating, we use the fomula=
p
1
!p
2
!p
3
!
n!
Total letter=n=5
As 4E are there,p
1
=4
Total arrangements=
4!
5!
Arranging remaining letters
Numbers we need to arrange=7+1=8
Since letter are repeating, we use this formula=
p
1
!p
2
!p
3
!
n!
Total letters=n=8
As 3N,2D
⇒p
1
=3,p
2
=2
Total arrangements=
3!2!
8!
Hence the required number of arrangement
=
3!2!
8!
×
4!
5!
=
3!2!
8×7×6×5×4×3!
×
4!
5×4!
=8×7×6×5×2×5=16800
verified_toppr