6 MRRM - Probability

R M R R M R RMRRMR is a string of 6 letters using M M 's and R R 's containing the substring ' M R R M MRRM '. M R M R M M MRMRMM is another string of 6 letters that does not contain M R R M MRRM . How many total 6 letter strings are there which contain M R R M MRRM as a substring?

24 8 12 16

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

David Vreken
Feb 24, 2020

There are 3 3 cases to consider for a string of 6 6 letters using only M M 's and R R 's to contain M R R M MRRM :

M R R M x x MRRMxx

x M R R M x xMRRMx

x x M R R M xxMRRM

where x x is either M M or R R . In each case, there are 2 2 choices for each x x , and the sequence of the substring M R R M MRRM ensures that there are no repeats, for a total of 3 × 2 × 2 = 12 3 \times 2 \times 2 = \boxed{12} possible strings.


The 12 12 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 \color{#3D99F6}MRRM \color{#333333}MM, \color{#3D99F6}MRRM \color{#333333}MR, \color{#3D99F6}MRRM \color{#333333}RM, \color{#3D99F6}MRRM \color{#333333}RR

M M R R M M , M M R R M R , R M R R M M , R M R R M R \color{#333333}M \color{#3D99F6}MRRM \color{#333333}M, \color{#333333}M \color{#3D99F6}MRRM \color{#333333}R, \color{#333333}R \color{#3D99F6}MRRM \color{#333333}M, \color{#333333}R \color{#3D99F6}MRRM \color{#333333}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 \color{#333333}MM \color{#3D99F6}MRRM, \color{#333333}MR \color{#3D99F6}MRRM, \color{#333333}RM \color{#3D99F6}MRRM, \color{#333333}RR \color{#3D99F6}MRRM

Great Solution!!

Mahdi Raza - 1 year, 3 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...