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:


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.

  • 2
    $\begingroup$ maybe a typo in the notes? $\endgroup$ – Alex Mar 7 '17 at 13:01
  • 1
    $\begingroup$ I think ur answer is right $\endgroup$ – Kiran Mar 7 '17 at 13:02
  • $\begingroup$ @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 :) $\endgroup$ – Osheen Sachdev Mar 7 '17 at 14:51
  • 2
    $\begingroup$ 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. $\endgroup$ – N. Shales Mar 7 '17 at 16:21

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