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
= 10C4
By using the formula,
nCr = \( \dfrac{ n!}{r!(n – r)!}\)
10C4 = \( \dfrac{10! }{ 4! (10 – 4)!}\)
= 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.
= 8C2
By using the formula,
nCr = \( \dfrac{ n!}{r!(n – r)!}\)
8C2 = \( \dfrac{8! }{ 2! (8 – 2)!}\)
= 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.
= 8C4
By using the formula,
nCr =\( \dfrac{ n!}{r!(n – r)!}\)
8C4 = \( \dfrac{8! }{ 4! (8 – 4)!}\)
= 7×2×5
= 70 ways
The required no. of ways are 210, 28, 70.
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