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###### CAT DILR | CAT Previous year questions
CAT Questions

Solve this DILR Question on Security Scan from CAT 2017. You are expected to answer the questions that follow, based on the constraints given. Some constraints could be specific to each question. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

## CAT DILR : 2017 slot 2 questions

### Security Scan

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)

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##### Method of solving this Question From CAT DILR 2017 Actual CAT Question Paper

Detailed Explanation

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?"

##### Hence, the answer is "15 Possible Sequences".

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