Question

In how many ways can 5 books be selected from 8 different books so that.

(1) a particular book is always selected?

(2) a particular books is never selected?

Answer 1

Out of 8 different books, 5 books are to be selected.

(1) A particular book is always selected : If a particular book is always selected, then out of 7 remaining books, the remaining 4 books can be selected in ⁷C₄ ways.

∴ Total combinations = ¹C₁ × ⁷C₄

= 1 × \(\frac{7×6×5×4}{4×3×2×1}\)

= 35

(2) A particular book is never selected:

If a particular book is never selected, then out of the remaining 7 books, 5 books can be selected in ⁷C₅ ways.

∴ Total combinations = ⁷C₅

= \(\frac{7×6×5×4\times3 }{4×3×2×1\times1}\)

= 21