GATE | Gate IT 2007 | Question 29

When searching for the key value 60 in a binary search tree, nodes containing the key values 10, 20, 40, 50, 70 80, 90 are traversed, not necessarily in the order given. How many different orders are possible in which these key values can occur on the search path from the root to the node containing the value 60?
(A) 35
(B) 64
(C) 128
(D) 5040


Answer: (A)

Explanation: There are two set of values, smaller than 60 and greater than 60. Smaller values 10, 20, 40 and 50 are visited, means they are visited in order. Similarly, 90, 80 and 70 are visited in order.
= 7!/(4!3!)
= 35

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