in how many ways can you arranged 5 mathematics books, 4 science books, and 3 english books on a shelf such that books of the same subject are kept together?
Answers
Answer:3!=3*2*1=6 OR 1,03,680
Step-by-step explanation:
first lets club together the books of the same subjects now we have 3 groups-maths, english, science
these 3 groups have to be arranged in three places so it is 3!
if every book is different from each other then we can arrange books in all the groups
for maths we have 5 books and these can be arranged in 5! ways
for science we have 4 books which can be arranged in 4! ways
for english we have 3 books which can be arranged in 3! ways
as all these are necessary for an arrangement to form we will multiply all no. of ways i.e. 3! * 5! * 4! * 3!=6*120*24*6= 1,03,680
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Given,
Total types of books = 3
Total mathematics books = 5
Total science books = 4
Total english books = 3
To Find,
In how many ways given books can be arranged =?
Solution,
The number of ways to arrange 5 mathematics books = 5!
The number of ways to arrange 5 mathematics books = 120 ways
The number of ways to arrange 4 science books = 4!
The number of ways to arrange 4 science books = 24 ways
The number of ways to arrange 3 english books = 3!
The number of ways to arrange 3 english books = 6 ways
The number of ways to arrange books of 3 different subjects = 3!
The number of ways to arrange books of 3 different subjects = 6 ways
Total ways to arrange all books such that books of the same subject are kept together = 120 * 24 * 6 * 6 ways
Total ways to arrange all books such that books of the same subject are kept together = 103680 ways
Hence, we can arrange 5 mathematics books, 4 science books, and 3 english books on a shelf such that books of the same subject are kept together in 103680 ways.