Given:

Total number of books = 10

Total books to be selected = 4

**(i) **there is no restriction

Number of ways = choosing 4 books out of 10 books

= ^{10}C_{4}

By using the formula,

^{n}C_{r} = \( \dfrac{ n!}{r!(n – r)!}\)

^{10}C_{4} = \( \dfrac{10! }{ 4! (10 – 4)!}\)

= 10×3×7

= 210 ways

**(ii) **two particular books are always selected

Number of ways = select 2 books out of the remaining 8 books as 2 books are already selected.

= ^{8}C_{2}

By using the formula,

^{n}C_{r} = \( \dfrac{ n!}{r!(n – r)!}\)

^{8}C_{2} = \( \dfrac{8! }{ 2! (8 – 2)!}\)

= 4×7

= 28 ways

**(iii) **two particular books are never selected

Number of ways = select 4 books out of remaining 8 books as 2 books are already removed.

= ^{8}C_{4}

By using the formula,

^{n}C_{r} =\( \dfrac{ n!}{r!(n – r)!}\)

^{8}C_{4} = \( \dfrac{8! }{ 4! (8 – 4)!}\)

= 7×2×5

= 70 ways

The required no. of ways are 210, 28, 70.

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