Question

Anish wants to arrange 7 textbooks on his bookshelf at random. Of these textbooks, 3 are math textbooks, and 4 are science textbooks. What is the probability that the two subjects alternate on the bookshelf?

1/12

1/24

1/35

1/48

1/144

Answer 1

Total number of ways to arrange 7 books in a shelf

= 7!

= 5040

Now,

According to the question

Let 7 places to place books be numbered 1, 2, 3, 4, 5, 6, 7

And there is only one possible arrangement to place 3 math & 4 science textbooks with two subjects in alternate as:-

1 science

2 math

3 science

4 math

5 science

6 math

7 science

Now,

Total number of arrangement with alternate subject

= Number of ways to arrange 4 science books * Total number of ways to arrange 3 math books

= 4! * 3!

= 24 * 6

= 144 ways

So,

Probability that the two subjects alternate on the bookshelf