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}

 

Answers (1)

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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