From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be …

Question

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is:

Accepted Answer

From 6 different novels 4 novels can be chosen = ${}^6{C_4}$ ways

And from 4 different dictionaries 1 can be chosen = ${}^3{C_1}$ ways

$$\therefore$$ From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary can be chosen = $${}^6{C_4} \times {}^3{C_1}$$ ways

Let 4 novels are N1, N2, N3, N4 and 1  dictionary is D1.

Dictionary should be in the middle. So the arrangement will be like this

\_ \_ D1 \_ \_

On those 4 blank places 4 novels N1, N2, N3, N4 can be placed. And 4 novels can be arrange $4!$ ways.

$$\therefore$$ Total no of ways = $${}^6{C_4} \times {}^3{C_1}$$ $ \times 4!$

Solutions · 1