Hi exc4libur,
Working with the work JOHNSON and JONES, here are the probabilities for pairs of letters that do NOT match (the first letter in each pair comes from the word JOHNSON and the second comes from JONES):
(J)(not J) = (1/7)(4/5) = 4/35
(O)(not O) = (1/7)(4/5) = 4/35
(H)(not H) = (1/7)(5/5) = 5/35
(N)(not N) = (1/7)(4/5) = 4/35
(S)(not S) = (1/7)(4/5) = 4/35
(O)(not O) = (1/7)(4/5) = 4/35
(N)(not N) = (1/7)(4/5) = 4/35
Total = (6)(4/35) + (5/35) = 29/35 --> again, this is the probability of NOT having a matching pair of letters. You could technically 'combine' the two "O" calculations into one calculation and the two "N" calculations into one calculation (but the overall result would be the same).
Probability of having a matching pair of letters = 1 - 29/35 = 6/35
GMAT assassins aren't born, they're made,
Rich
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