JEE Main · 2009 · 12 Apr 2009 · Offline · Permutations and Combinations

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

(A)less than 500
(B)at least 500 but less than 750
(C)at least 750 but less than 1000
(D)at least 1000✓ Correct

Answer: (D)

Solution

Choose the 4 novels from 6 in

(4 6) = 15

ways and the 1 dictionary from 3 in

(1 3) = 3

ways. With the chosen dictionary pinned to the middle spot, the four novels fill the remaining four places in

4! = 24

orders. The total number of arrangements is

15 \times 3 \times 24 = 1080

, which is at least a thousand.

JEE Main · 2009 · 12 Apr 2009 · Offline · Single correct option

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