ME test

Question

The number of ways to choose 'n' items from '2n' items of which 'n' are alike and rest are unlike is _________?

A) 2ⁿ                       B) 2ⁿ-1

C)  (2ⁿ).²ⁿC_n                D) ²ⁿC_n      

Comments

is it A?

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Yep can u explain?

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https://gateoverflow.in/113040/permutation-and-combinations

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Thank you :)

Answer 1

Select 0 item from n identical items (only in 1 way), rest n items from n distict items in $\binom{n}{n}$ways 

OR

Select 1 item from n identical items(only in 1 way) , rest n-1 items from n distict items in $\binom{n}{n-1}$ ways 

OR

Select 2 item from n identical items (only in 1 way), rest n-1 items from n distict items in $\binom{n}{n-2}$ ways 

.

.

.

OR

Select n item from n identical items (only in 1 way), rest 0 items from n distict items in $\binom{n}{0}$ways 

So. total = nCn + nC(n-1) + nC(n-2) + ...+ nC0 = 2ⁿ

Comments

Thanks nicely explained :)