Question: The lab has decided to allow variations of the original sequence so that input of the scanned sequence of five fingers is allowed to vary from the original sequence by one place for any of the fingers. Thus, for example, if TIMRL is the original sequence, then ITRML is also allowed, but LIMRT is not.
How many different sequences are allowed for any given person’s original scan?
Let us suppose that the original sequence is TIMRL. As per the condition given in the question, for any of the given fingers, the scanned sequence is allowed to vary by one place for any of the given fingers. So for the sequence TIMRL, we can have the following possibilities of sequence of scans, so that it is accepted.
1] All the letters of original sequence are in place. This is possible in 1 way.
2] T & I get interchanged – 1 way
3] T & I and M & R get interchanged – 1 way
4] T & I and R & L interchanged – 1 way
5] Only R & L get interchanged – 1 way
6] Only M & R get interchanged – 1 way
7] I & M get interchanged – 1 way
8] I & M and R & L get interchanged – 1 way
So a total of 8 different sequences of scans will be accepted.
Hence, option (c).