Question

In how many ways can Anna arrange 2 math books, 3 physics books, and 5 chemistry books on her shelf if all books of the same subject must be adjacent? (The books are distinguishable.)

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Answer 1

• 2 maths books can be arranged as (2!=2) ways
• 3 physics books can be arranged as (3!=6) ways
• 5 chemistry books can be arranged as (5!=120) ways
• Books can be arranged in suject-wise in (3!=6) ways

Hence, total ways are (2×6×120×6) ways =8640 ways.

8640 is the right answer.

Answer 2

• 8640 ways

Explanation:

Arranging the books of each subject:

Math:

• Combination of 2 books → 2! = 2

Physics:

• Combination of 3 books → 3! = 6

Chemistry:

• Combination of 5 books → 5! = 120

We also need to consider the subjects.

There are 3 subjects, kept separately, they will be arranged in 3! = 6 ways

So the total number of combinations is:

• 2*6*120*6 = 8640