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

English

Gujarati

Hindi

6.Permutation and Combination

hard

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. The number of such arrangements is :

A

less than $500$

B

at least $500$ but less than $750$

C

atleast $1000$

D

at least $750$ but less than $1000$

(AIEEE-2009) (JEE MAIN-2018)

Solution

$\therefore $ Required number of ways ${ = ^6}{C_4}{ \times ^3}{C_1} \times 4!$

$ = 15 \times 3 \times 24 = 1080$

Standard 11

Mathematics

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