CAT DI LR section has become increasingly tough beginning from 2015.This involves solving Actual CAT sets from the CAT Exam from CAT Question paper - 2017 - Slot 2. Detailed Video explanation is provided for this CAT LR DI puzzle, try to solve this before you jump into the Solution for this Actual CAT Question from DI LR.
A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands. When an employee first joins the lab, her fingers are scanned in an order of her choice, and then when she wants to re-enter the facility, she has to scan the five fingers in the same sequence.
The lab authorities are considering some relaxations of the scan order requirements, since it is observed that some employees often get locked-out because they forget the sequence.
Question 3: The lab has now decided to require six scans in the pass sequence, where exactly one finger is scanned twice, and the other fingers are scanned once, which can be done in any order. For example a possible sequence is TIMTRL. Suppose the lab allows a variation of the original sequence (of six inputs) where at most two scans are out of place, as long as the finger originally scanned twice is scanned twice and other fingers are scanned once. How many different sequences of scans are allowed for any given person's original scan? (TITA)
This is very similar to the first one except that there are six slots. So, let us jump to the more mathematical approach. Suppose we started with TIMTRL. We need to swap some two of these six. This can be selected in 6C2 ways. OR 15 ways totally. However, sitting inside this 6C2 would be the selection of 2 T’s swapping which will not really give us a new sequence. So, we need to subtract this.
Number of new options is 6C2 -1 = 14.
Total number of possible sequences = 14 + 1 = 15.
The question is "How many different sequences of scans are allowed for any given person's original scan?"
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