+4 How many combinations of 5 dominoes can be taken from a set of 28 such that 3 dominoes has a same number in it.
The dominoes are formed as followes.
Each domino will have 2 numbers in it. The numbers will be any in between 0 and 6 (both included). There will be exactly one domino that has a number pair of any 2 in between 0 and 6. Hence there will be 7 dominoes for each number. And all the dominoes will be unique
Domino combinations
0-0, 0-1, 0-2, 0-3, 0-4, 0-5, 0-6
1-1, 1-2, 1-3, 1-4, 1-5, 1-6
2-2, 2-3, 2-4, 2-5, 2-6
3-3, 3-4, 3-5, 3-6
4-4, 4-5, 4-6
5-5, 5-6
6-6
A total of 28
In which 5 random dominoes are selected such that 3 dominoes has a same number in it. Eg: 3-5, 3-4, 3-6, 2-1, 4-4.
I also want to know how many combinations of 5 dominoes will be there such that
1) 4 has same number (0-1, 0-2, 0-3,0-4,1-1 -- Four dominoes has 0 in it)
2) The number are in a sequence (0-1,4-2,5-3,1-4,5-5 -- The second numbers are in a seuence)
3) All 5 has the same number (1-1, 1-3,1-5,1-6,1-4)
4) 3 same numbers and the other 2 is a different-same number (2-2, 2-3, 2-4, 4-1,4-5 -- First three has '2' common and the remaining 2 has '4' common)
5) There are 2 pairs of same number and an alternate number (2-1, 2-2, 3-3, 3-4, 6-6 -- First 2 has '2' common and the third and forth has 3 common)
Thanks
Rineesh
