How many distinct binary search trees can be created out of 4 distinct keys?

Correct Answer (Detailed Explanation is Below)

C. 14

Detailed Explanation

Explanation:

The number of distinct Binary Search Trees (BSTs) that can be formed with n distinct keys is given by the Catalan Number formula.

For $n$ keys:

$$C_n = \frac{(2n)!}{(n+1)! \, n!}$$

For n = 4:

$$C_4 = \frac{(8)!}{5! \times 4!} = 14$$

So, 14 different BSTs can be formed using 4 distinct keys.