# Find the number of ways in which RESONANCE can be arranged so that letters R,S,O,A appear in the order same as in the word RESONANCE

Find the number of ways in which RESONANCE can be arranged so that letters R,S,O,A appear in the order same as in the word RESONANCE

My working:

R
EE
S
O
NN
A
C

The number of such ways should simply be 4! divided by the total permutations i.e. =$\frac{9!}{2!2!4!}=3780$

But the answer is supposed to be $3870$ and I can't figure out why.

• maybe a typo in the notes? – Alex Mar 7 '17 at 13:01
• I think ur answer is right – Kiran Mar 7 '17 at 13:02
• @Alex I don't know...it was an mcq with both these options, and the one I ticked was wrong. Though I haven't really encountered any errors in the answers till now, maybe it's just a mistake like you said :) – Osheen Sachdev Mar 7 '17 at 14:51
• Agreed. $9!/(2!^24!)$ is undoubtedly correct. It is easy to confuse those two numbers due to the transposition of 8 and 7. Do make sure you are reading everything correctly, although I suspect you are and it is their mistake. – N. Shales Mar 7 '17 at 16:21