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How many different selections of 4 books...

How many different selections of 4 books can be made from 10 different books, if There is no restriction Tow particular books are always selected; Two particular books are never selected?

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Two particulars books are never selected from 10 books. So, 4 books need to be selected from 8 books. Required number of ways if two particular books are never selected `= ^8 C_4=\frac8(4 )\times \frac7(3) \times \frac6(2) \times \frac 5(1)=70`
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Knowledge Check

  • There are 10 different books in a shelf. The number of ways in which three books can be selected so that exactly two of them are consecutive is

    A
    `60`
    B
    `54`
    C
    `56`
    D
    `36`

  • There are 100 different books in a shelf. Number of ways in which 3 books can be selected which are not neighbours is

    A
    `""^(100)C_(3) - 98`
    B
    `""^(97)C_(3) `
    C
    `""^(96)C_(3)`
    D
    `""^(98)C_(3)`

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