Out of $6$ books, in how many ways can a set of one or more books be chosen

  • A

    $64$

  • B

    $63$

  • C

    $62$

  • D

    $65$

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In a shop there are five types of ice-creams available. A child buys six ice-creams.               

Statement $-1 :$ The number of different ways the child can buy the six ice-creams is $^{10}C_5.$ 

Statement $-2 :$ The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging $6 \,A's$ and $4 \,B's$ in a row.

  • [AIEEE 2008]