The sample space has 6^5 entries. Among them, the pattern 11122 has (taken 2 out of 5 ) [I cannot type the combinatoric symbols in this window] or 5x4/2 =10 entries, this is to fix the two locations out of 5 for "2" . There are 6 possibilities for "111" , i.e. "111", "222", ..., "666" . For each of them, there are 5 possibilities for "22", i.e. associated with "111", we have "22", "33", ..., "66". Hence, all together we have 6x5 patterns like "11122". The total number of qualified entries is 10x6x5. The probability is 10x6x5/ (6^5 ) = 25/648. |
