# Permutation and Combinations

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The number of ways to choose n things from 2n things of which n are alike and rest are unlike?

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Yes @Rahul. Could you please explain the methodology to solve?

We will have to take all cases in which we select one "indistinguishable" item, 2 "indistinguishable" item and so on till n "instinguishabe item.

Let indistinguishable item be k-set items, distinct items be s-set items.( or vice versa it will not change answer)

When we select 0 item from set of k-items then we can have n from s-items, when 1 item from set of k-items then n-1 from s-set and so on......

So total ways is,

nC​​​​​​​​​​​​nC​​​​​​​​​​​.............+nC= 2(binomial)

http://mathcentral.uregina.ca/QQ/database/QQ.09.08/h/chinonyerem1.html

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## Related questions

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My approach :- ways to arrange 6 distinct symbols = 6! Place 2 blanks between each symbol, remaining blanks = 2 Now these 2 blanks can be placed in any of 5 places so = 5*5= 25 ways Total ways = 6!*25 = 18000 But the answer given in 10800 :( please someone tell me where I am wrong.