Multiple choice

There are 5 English, 4 Sanskrit and 3 Telugu books. Two books from each group are to be arranged in a shelf. The number of possible arrangements is:

  1. $(180) 6!$
  2. $(12) 7!$
  3. $7!$
  4. $180$
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A Correct answer
Explanation

Number of ways to choose 2 books from each group: C(5,2) * C(4,2) * C(3,2) = 10 * 6 * 3 = 180. These 6 chosen books can be arranged in 6! ways. Total arrangements = 180 * 6!.

AI explanation

First, select the books from each group using combinations: 5C2 for English, 4C2 for Sanskrit, and 3C2 for Telugu. This yields 10 multiplied by 6 multiplied by 3, which equals 180 ways to choose the six books. These six selected books can then be arranged on the shelf in 6! ways, making the total arrangements 180 multiplied by 6!.