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The total different ways that can the letters in the word

"ARRANGEMENT"

to be arranged in 11 letters is:

$$\frac{11!}{2!\times2!\times2!\times2!}=2494800\space ways $$

But how many different ways can the letters be arranged in only 5 letters?

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    $\begingroup$ Hi and welcome to the site! Since this is a site that encourages and helps with learning, it is best if you show your own ideas and efforts in solving the question. Can you edit your question to add your thoughts and ideas about it? $\endgroup$ – 5xum Nov 9 '16 at 11:44
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    $\begingroup$ Also, don't get discouraged by the downvote. I downvoted the question and voted to close it because at the moment, it is not up to site standards (you have shown no work you did on your own). If you edit your question so that you show what you tried and how far you got, I will not only remove the downvote, I will add an upvote. $\endgroup$ – 5xum Nov 9 '16 at 11:44
  • $\begingroup$ I would also strongly recommend using the search feature. You can often find a similar question like this one which might help you to answer your own question. $\endgroup$ – Ian Miller Nov 9 '16 at 11:47
  • $\begingroup$ More than 3 :) , less than there are atoms in the universe $\endgroup$ – Pieter21 Nov 9 '16 at 11:50
  • $\begingroup$ @HoChungYin Great first edit. Now what have you tried? And where did you get stuck? $\endgroup$ – Ian Miller Nov 9 '16 at 12:30
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The $$\frac{11!}{2!^4}$$ part is already right.

To divide it in 5 words, you have to multiply by:

$${{6 + 4}\choose{4}}$$

Given that words have at least 1 letter, you have $11 - 5 = 6$ letters left to divide over 5 buckets for 0 or more letters.

This is typically done with an eggs in baskets calculation with bars: you have to place 4 bars between the eggs (letters in this case). Out of 10 positions, you have to select 4 bars.

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