Number of ways of choosing 10 objects out of 31 objects of which 10 are identical and remaining 21 a

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6.Permutation and Combination

hard

The number of ways of choosing $10$ objects out of $31$ objects of which $10$ are identical and the remaining $21$ are distinct, is

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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