Correct Answer - Option 4 : 1440
No. of letters in the word 'STRANGE' = 7
Since, 'GE' in the word can not be separated, so consider them as one letter.
Now, no. of letters in the word 'STRANGE' = 6, which are S, T, R, A, N and (GE)
So, total arrangements possible = Arrangement possible with 6 letters × No. of ways in which (GE) can be arranged within them
= (6!) × (2!)
= (6 × 5 × 4 × 3 × 2 × 1) × ( 2 × 1)
= 720 × 2
= 1440
ALTERNATE SOLUTION:
No. of letters in the word 'STRANGE' = 7
Since, 'GE' in the word can not be separated, so consider them as one letter.
Now, no. of letters in the word 'STRANGE' = 6, which are S, T, R, A, N and (GE)
Let there be 6 blanks available for each letter, then
First blank can be filled by → 6 letters
Second blank can be filled by → 5 letters
Third blank can be filled by → 4 letters
Fourth blank can be filled by → 3 letters
Fifth blank can be filled by → 2 letters
Sixth blank can be filled by → 1 letter
Multiplying them, we get = 6 × 5 × 4 × 3 × 2 × 1 = 720
And GE can be arranged in 2 ways, that are- (GE) and (EG)
So, 720 × 2 = 1440
Hence, the letters of the word 'STRANGE' can be arranged in 1440 ways such that the 'GE' in the word will always come together.
