# 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?

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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?

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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