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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 1: The lab has decided to allow a variation in the sequence of scans of the five fingers so that at most two scans (out of five) are out of place. For example, if the original sequence is Thumb (T), index finger (I), middle finger (M), ring finger (R) and little finger (L) then TLMRI is also allowed, but TMRLI is not. 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

Let us start with the original sequence of TIMRL and then think of different variations. We can have a scenario where T & I are interchanged, then T & M being interchanged, then T & R, and so on. Or, we can have ITMRL, MITRL, RIMTL and LIMRT. Post this, we can keep T at the same slot and swap I and something else. This way, we will get TMIRL, TRMIL, TLMRI. Post this, we can move to swapping M with something else. We will get TIRML, TILRM. Finally, we can have TIMLR.

Totally we can have
ITMRL, MITRL, RIMTL and LIMRT.
TMIRL, TRMIL, TLMRI.
TIRML, TILRM.
TIMLR.

Or a total of 4 + 3 + 2 + 1 = 10 possibilities. Remember that we need to include the original as well. So, we will have a total of 11 possibilities!

The question is "How many different sequences of scans are allowed for any given person's original scan?"

Hence, the answer is "11 Possible Sequences".

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