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Type the odd characters out in each group: abz2a 125t7 HhHaHh year.s 5433r21 worl3d

location: FAQ / combinatorics / others

One instance of 3 reps and one instance of 4 reps

An example of one instance of 3 reps is AAAABC. There are (6 choose 2) possible positions of the two non-repeated stimuli in a sequence of length 6. These are 

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There are 92 possible stimuli and the two stimuli must be distinct from each other and the repeated stimulus. This gives 92x91x15x90 combinations and a probability, dividing by $$926 $$ , of 0.00001.

For one instance of 4 reps e.g. ABBBBB there are 6 possible positions for the non-repeated stimulus (each of the 6 positions in the sequence). There are 92 possible stimuli and the repeated and non-repeated stimuli must be different giving 92x6x91 possible combinations and a probability, dividing by $$926 $$ , of 0.00000008. There can be no more than one instance of 3, 4 or 5 reps so the above scenarios cover all the possibilities for 3 and 4 reps respectively since there is only a single instance possible of 3, 4 or 5 reps.