CAT 2017 Slot 2 DILR · Question 27
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.
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)
Type-in answer (TITA): no options, no negative marking.
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