Security Scan
CAT 2017 Slot 2 · DILR · Medium · Permutations
Passage / data set
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. 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.
Question 1 of 4
How many different sequences of scans are allowed for any given person's original scan?
11
Explanation
Sequences with 0 out of place: 1. Sequences with 1 out of place: 0 (impossible). Sequences with 2 out of place: . Total allowed sequences = .
Question 2 of 4
How many different sequences are allowed for any given person's original scan?
- A.
7
- B.
5
- C.
8
- D.
13
D
Explanation
Considering modified rules in the variants, total valid sequences equals 13.
Question 3 of 4
How many different sequences of scans are allowed for any given person's original scan?
15
Explanation
Under the modified question conditions, total allowed sequences equal 15.
Question 4 of 4
How many different sequences of scans are allowed if the original scan sequence is LRLTIM?
- A.
8
- B.
11
- C.
13
- D.
14
C
Explanation
For sequence LRLTIM with repeated letters, the number of distinct valid permutations is 13.
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