Question -
Answer -
Given:
Total number of books= 10
Total books to beselected = 4
(i) there is norestriction
Number of ways =choosing 4 books out of 10 books
= 10C4
By using the formula,
nCr = n!/r!(n – r)!
10C4 = 10! / 4! (10 – 4)!
= 10! / (4! 6!)
= [10×9×8×7×6!] / (4!6!)
= [10×9×8×7] /(4×3×2×1)
= 10×3×7
= 210 ways
(ii) two particular booksare 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 = n!/r!(n – r)!
8C2 = 8! / 2! (8 – 2)!
= 8! / (2! 6!)
= [8×7×6!] / (2! 6!)
= [8×7] / (2×1)
= 4×7
= 28 ways
(iii) two particular booksare never selected
Number of ways = select4 books out of remaining 8 books as 2 books are already removed.
= 8C4
By using the formula,
nCr = n!/r!(n – r)!
8C4 = 8! / 4! (8 – 4)!
= 8! / (4! 4!)
= [8×7×6×5×4!] / (4!4!)
= [8×7×6×5] /(4×3×2×1)
= 7×2×5
= 70 ways
∴ The required no.of ways are 210, 28, 70.