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Choose the correct option.
How many words can be formed using the letters of the word "CORRESPONDANCE" if the consonants are always written together?
A182
B184
C216*9!
DNone of these
Answer: Option (Login/Signup)
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STEP-BY-STEP
Acc. to the question, the word can be split up into two halves , (CRRSPNDNC) &(OEOAE)
Now these two can be arranged among themselves in 2! Ways.
Now (CRRSPNDNC) can be arranged in 9!/(2!*2!*2!) ways
Similarly (OEOAE) can be done in 5!/(2!*2!) ways.
When all 3 cases put together= 2!* 9!/(2!*2!*2!)* 5!/(2!*2!)= (5!/16)*9! = 7.5*9!
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STEP-BY-STEP
Acc. to the question, the word can be split up into two halves , (CRRSPNDNC) & (OEOAE)
Now these two can be arranged among themselves in 2! Ways.
Now (CRRSPNDNC) can be arranged in 9!/(2!*2!*2!) ways
Similarly (OEOAE) can be done in 6!/(2!*2!) ways.
When all 3 cases put together= 2!* 9!/(2!*2!*2!)* 6!/(2!*2!)= 45*9!
Now these two can be arranged among themselves in 2! Ways.
Now (CRRSPNDNC) can be arranged in 9!/(2!*2!*2!) ways
Similarly (OEOAE) can be done in 6!/(2!*2!) ways.
When all 3 cases put together= 2!* 9!/(2!*2!*2!)* 6!/(2!*2!)= 45*9!
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