is a string of 6 letters using 's and 's containing the substring ' '. is another string of 6 letters that does not contain . How many total 6 letter strings are there which contain as a substring?
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There are 3 cases to consider for a string of 6 letters using only M 's and R 's to contain M R R M :
M R R M x x
x M R R M x
x x M R R M
where x is either M or R . In each case, there are 2 choices for each x , and the sequence of the substring M R R M ensures that there are no repeats, for a total of 3 × 2 × 2 = 1 2 possible strings.
The 1 2 strings are:
M R R M M M , M R R M M R , M R R M R M , M R R M R R
M M R R M M , M M R R M R , R M R R M M , R M R R M R
M M M R R M , M R M R R M , R M M R R M , R R M R R M