Permutation and Combinations

Question

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

Comments

A is the answer???

---

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

Answer 1

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_{​​​​​​^{​​​​​​}0} + ⁿC₁ + _{​​​​​}​​​​​​.............+ⁿC_n = 2ⁿ (binomial)

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