Count By Unique Entries

I am hoping this can be done with formulae. Starting at C7 and continuing down the C column there is a list of names which could potentially run from C7 to C5000. This list of names will contain duplicates. For each name there is a corresponding 'reason' in the F column which will contain the word 'Truancy' or 'Late'.

I need a formula that can count the number of UNIQUE names in the C column which correspond to the word 'Truancy' or 'Late' in the E column.

An example,

[Name].....................[Reason]
C7 ...........................E7
John Potts.................Truancy 2
Matt Jones................Truancy 10
John Potts.................Truancy 4
Matt Jones ...............Late AM
Pete Burns................Late PM
Pete Burns ...............Late Both
Steve Lopez..............Truancy 6

Count of unique names with the word Truancy in the corresponding E column = 3 [John Potts has 2 instances of the word truancy in column E but this is only counted once]

Count of unique name with the Word Late in the corresponding E column = 2 [Pete Burns has 2 instances of the word late in the E column but this is only counted once].

I have also included a sample workbook.