Question

20160
Determine the number of ways to arrange HACKEREARTH so that all the vowels are placed adjacent to each other?
10080
O 120960
60480
W
Submit​

Answer 1

Given  :   HACKEREARTH  

To Find :  number of ways to arrange HACKEREARTH so that all the vowels are placed adjacent to each other?

20160

10080

120960

60480

Solution:

HACKEREARTH  

Vowels  - 4

A = 2

E = 2

Consonants = 7

H - 2

R - 2

K , C , T - 1

all the vowels are placed adjacent to each other

Take them as 1  and 4 vowels can be arranged in 4!/2!2!  = 6 ways

as A & E are repeated

now 7 consonants  + 1 ( group of vowels) can be arranged in 8! ways

but H and R is repeated twice

so 8!/2!2!  

Total arrangements = 6 x 8!/2!2!  

=60480

60480 umber of ways to arrange HACKEREARTH so that all the vowels are placed adjacent to each other

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