Use combinations to find the number of ways 10 books 3 math

Use combinations to find the number of ways 10 books (3 math, 3 science, and 4 English) can be arranged on a book shelf where all three of the math books and all three of the science books must be together (however, the math and science books do not need to be next to each other, but they can be).

Solution

10 books

3 math, 3 science 4 english

3 math and 3 science together constitute 2 units.

Thus totally there are 3 math, 3 scien and 4 english separate thus 6 units

They can be arranged in 6! ways

3 math among itself in 3! ways similarly science

Hence total ways = 6!(3!)(3!)