Home
Class 12
MATHS
From 6 different novels and 3 different ...

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

A

atleast 1000

B

less than 500

C

atleast 500 but less than 750

D

atleast 750 but less than 1000

Text Solution

Verified by Experts

The correct Answer is:
A
Given 6 different novels and 3 different dictionaries.
Number of ways of selecting 4 novels from 6 novels is
`""^(6)C_(4) = (6!)/(2!4!) = 15`
Number of ways of selecting 1 dictionary is from 3 dictionaries is `""^(3)C_(1) = (3!)/(1!2!) = 3`
`therefore` Total number of arrangement of 4 novels and 1 dictionary where dictionary is always in the middle, is
`15 xx 3 xx 4! = 45 xx 24 = 1080`
Promotional Banner

Similar Questions

Explore conceptually related problems

Arrange the following words as per order in the dictionary. 1. Pearl 2. Peasant 3. Pea 4 . Peanut .

Arrange the following words as per order in the dictionary: 1. Centre 2. Center 3. Central 4. Centrum

Arrange the following words as per order in the dictionary: 1.Still 2. Stifile 3. Stink 4. Stingy

Arrange the following words as per order in the dictionary: 1. Zeal 2. Zebra 3. Zygote 4. Zinc 5. Zest

Different words are being formed by arranging the letter of the word 'ARRANGE' Q. The rank of the word 'ARRANGE' in the dictionary is

Arrange the following words as per order in the dictionary: 1. Manifest 2. Meticulous 3. Meridian 4. Merchant

Arrange the following words as per order in the dictionary 1. Weather 2. Weasand 3. Wealth 4. Weapon 5. Weekend