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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 a shelf so that the dictionary is always in the middle. Then the number of such arrangements is -

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 -

Grade:12

4 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
select 4 novels from 6 novels =6c4
select 1 dictionary from 3 =3c1
as always dictionary should be in the middle NNDNN is arrangement
so 6c4* 3c1 *4! *1!=1080
Thanks and Regards
Shaik Aasif
askIITians Faculty
shiva kumar
15 Points
5 years ago
The given question can be answered as 
               d1                 =6p4 
Like this we can arrange other two dictionaries 
i.e, 3(6p4)=1080
Hence proved.
 
Vadla Bhanu prasad
13 Points
4 years ago
We have to select 4 novels from 6 novels
No of ways of selecting is 6c4.and no.of ways of selecting 1 dictionary out of 3 was 3c1.
Total ways =6c4✖️3c1.
In shelf one dictionary placed at middle in 1 way.
4 novels arranged in 4 position s in 4! Ways.
The total no.of ways is equal to
6c4✖️3c1✖️4!✖️1=1080
Therefore atleast 1000arrangements are possible
ankit singh
askIITians Faculty 614 Points
3 years ago

anation:

We're picking 5 books in total. The dictionary will be the middle book so let's look at that first.

There are 3 different dictionaries to pick from, and so the number of choices for that middle book is 3.

The remaining 4 spots for books will be chosen from a population of 6. We can use the permutation formula (P6,4=6!2!=6×5×4×3=360).

All told, there is 3×360=1080 ways to arrange the books.

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