Q

# Help me solve this - Permutations and combinations - JEE Main

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

• Option 1)

$2^{20}-1$

• Option 2)

$2^{20}+1$

• Option 3)

$2^{21}$

• Option 4)

$2^{20}$

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No. of ways

$\left(^{21}C_0+..........+^{21}C_{10}\right)+\left(^{21}C_{10}+^{21}C_9+.........+^{21}C_0\right)=2^{21}$

$^{21}C_0+.....+^{21}C_{10}=2^{20\;\;\;\;\\;\;\;}$

Option 1)

$2^{20}-1$

Option 2)

$2^{20}+1$

Option 3)

$2^{21}$

Option 4)

$2^{20}$

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