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How many distinct three-letter sequences with at least one “T” can be formed by using three of the six letters of TARGET? One such sequence is “T-R-T.”

 Nov 3, 2019
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Sequences with one T  =

(TAR)  (TAG) (TAE)

(TRG) (TRE)

(TGE)

 

And each of these can be arranged in 6 ways....so....6 * 6  =   36       (!)

 

Sequences with two T's  =

(TTA) (TTR) (TTG) (TTE)

And each of these can be arranged in 3 ways ,,,,so   4 * 3  =  12     (2)

 

So...adding (1)  and (2)   we get  48 arrangements with at least one T

 

cool cool cool

 Nov 3, 2019

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