6.Permutation and Combination
hard

$31$ વસ્તુ પૈકી $10$ સમાન વસ્તુ છે અને $21$ ભિન્ન વસ્તુ છે તેમાથી $10$ વસ્તુની પસંદગી કેટલી રીતે કરી શકાય.

A

$2^{20}$

B

$2^{20}+1$

C

$2^{21}$

D

$2^{20}-1$

(JEE MAIN-2019)

Solution

Since $^{21}{C_0} + …..{ + ^{21}}{C_{10}}{ + ^{21}}{C_{11}} + …..{ + ^{21}}{C_{21}} = {2^{21}}$

$ \Rightarrow $ but we have to select $10$ objects and $^{21}{C_0} + …..{ + ^{21}}{C_{10}}{ + ^{21}}{C_{11}} + …..{ + ^{21}}{C_{21}}$

$\left( {^{21}{C_0} + …..{ + ^{21}}{C_{10}}} \right) = {2^{10}}$

Standard 11
Mathematics

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