question_answer

The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is:                                                       [JEE Main Held on 12-4-2019 Morning]

A) \[{{2}^{20}}\]         

B) \[{{2}^{20}}-1\]

C) \[{{2}^{20}}+1\]                

D) \[{{2}^{21}}\]

Correct Answer: A

Solution :

\[^{21}{{C}_{0}}+....{{+}^{21}}{{C}_{10}}{{+}^{21}}{{C}_{1}}+......{{+}^{21}}{{C}_{0}}={{2}^{21}}\] \[{{(}^{21}}{{C}_{0}}+....{{+}^{21}}{{C}_{10}})={{2}^{20}}\]