Tough probability question (urgent)?

Posted on 2016-11-16 18:52:00 in Math by LYAND

I have thoughts about it, I tried few times but I couldn't get the result, so I'm in need of help. 

There is a pen case which contains 11 pens each belong to each man. So 11 men pick a pen from the case in order. The first man picks a pen randomly,then he leaves. The second one picks his own pen if he sees it, and he picks a pen randomly if he doesn't see his own pen. The third picks his own pen if he sees it;if he doesn't, he picks a pen randomly, and so on. What is the probability that the eleventh man picks his own pen? 

The trick is that the first guy picks a pen randomly, but the rest picks their own if they see it. Hence, if the first guy picks his pen the rest picks their own thus the probability is 1/11. However it gets tougher if the first guy doesn't pick his own pen. Any idea how this can be found? 

Thanks for any help.

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