Question

There are 4 different books of Statistics and 3 different books of Economics on a table. In how many ways can 2 books be selected such that –

(i) both the books are of the same subject?
(ii) both the books are of different subject?
(iii) no book of Economics is selected?

Answer 1

There are 4 different books of Statistics and 3 different books of Economics on a table.

(i) Both the books are of the same subjects: 2 books of Statistics out of 4 books can be selected in ⁴C₂ ways or 2 books of Economics out of 3 books can be selected in ³C₂ ways.

∴ Total combinations = ⁴C₂ + ³C₂
= \(\frac{4×3}{2×1}+\frac{3×2}{2×1}\)
= 6 + 3
= 9

(ii) Both the books are of different subject:
one book of Statistics out of 4 books can be selected in ⁴C₁ ways and one book of Economics out of 3 books can be selected in ³C₁ ways.

Total combinations = ⁴C₁ × ³C₁ = 4 × 3 = 12

(iii) No book of Economics is selected: All two books of statistics out of 4 books can be selected in ⁴C₂ ways and no book of Economics in ³C₀ ways.

Total combinations = ⁴C₂ × ³C₀

= 6 × 1 = 6