Question

In how many ways can a hotel owner subscribe 3 newspapers and 2 magazines from 8 different newspapers and 5 different magazines available in the city? If a particular newspaper is to be selected and a particular magazine is not to be selected then in how many ways can this selection be done?

Answer 1

8 different newspapers and 5 different magazines are available in the city.
A hotel owner can subscribe 3 newspapers out of 8 newspapers in ⁸C₃ ways and 2 magazines out of 5 magazines in ⁵C₂ ways

∴ Total combination = ⁸C₃ × ⁵C₂

= \(\frac{ 8×7×6}{3×2×1}+\frac{5×4}{2×1}\)

= 56 × 10 = 560

If a particular newspaper is to be selected then 2 newspapers out of the remaining 7 newspapers can be subscribed in ⁷C₂ ways and a particular magazine is not to be selected then 2 magazines out of the remaining 4 magazines can be selected in ⁴C₂ ways.

∴ Total combinations = ⁷C₂ × ⁴C₂

= \(\frac{7×6}{2×1}×\frac{4×3}{2×1}\)

= 21 × 6

= 126