In how many ways can 12 similar balls be divided into three groups ,with each group containing at most six balls
Answers
660,651,642,633,624,615,606,561,552,543,534,525,516,462,453,444,435,426,363,354,345,336,264,255,246,165,156
so no of ways are 27
Answer:
There are 6 ways.
Step-by-step explanation:
If at least three groups contain
Only 1 ball, the other two groups must have content the remaining 11 balls, that can only be medium large group with 5 and largest group with 6.
These 3 groups have sizes 1, 5 and 6.
If at least three groups contain 2 balls, the other two groups must have content another 10 balls, it can be two manners.
A medium group can have 4 and the largest group has 6. Or can everyone have 5:
These 3 groups have sizes 2, 4 and 6.
These 3 groups have sizes 2, 5 and 5.
If at least three groups contain
3 balls, the other two groups must have content another 9 balls, it can be two manners.
The second group can also have 3 and largest group 6. Or medium size
group can have 4 and largest group 5.
These 3 groups have sizes 3, 3 and 6.
5. These 3 groups were sizes 3, 4 and 5.
Another way. Each can have 4 balls:
6. 3 groups have sizes 4, 4 and 4.
That there are 6 ways to divide 12 balls into 3 groups,
without group greater than 6.
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