Question: The lab has decided to allow a variation in the sequence of scans of 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?
As per the given information either the entire sequence of scans has to be correct or 3 out of the 5 scans have to be in place. So if we consider TIMRL as the original sequence, each of T, I, M, R and L has to be in the correct sequence which is only possible in 1 way. Now if the sequence of scans is out of place, then at least 2 scans will have to be out of place. Which implies that 3 scans are in place. So 3 out of T, I, M, R and L are in place. Now this is possible in 5 C3 or 10 ways. So number of different sequences of scans that are allowed = 1 + 10 = 11 ways.