# Math Help - Calculating the amount of possibilities

1. ## Calculating the amount of possibilities

Hi there,

I need some help to resolve a problem... Let's say that I have 30 options spread in 3 blocks where a person need to choose 10 options according to these rules:
1. The person can only choose 3 options in the last block
2. The person can only choose 3 options in the second block
3. There is no maximum related to the first block
4. The previous block must always have equal or less options chosen (example: cannot take 3 options in 3rd block if 2nd block has only 2 options picked)
5. The number of options per block is variable, for the first sequence the 1st block could have 10, for the 2nd sequence the 1st block could have 7 etc.
6. An option can be picked only once

If someone might have some idea on how to resolve this, I'd really appreciate it.

Thanks !

2. ## Re: Calculating the amount of possibilities

Well consider the same question but with few differences:
4 options and you have to choose 3 only and you have 3 option boxes and the same rule set where box 3 has to have the same or less number of options as box2
box1 box2 box3
1. 3 0 0
2. 2 1 0
3. 1 1 1

Now then. Lets call the 4 options a,b,c, and d. Scenario 1 would have 4C3 possibilites only which is 4(there are 4 ways to choose 3 options I am assuming the order in these boxes do not matter)
Option 2 would have 4C2*2C1 possibilities which is 12(The theory here is that you choose 2 in the first box and then from the remaining two you have only one option to choose from)
ab c
ab d
ac b
ac d
and so on...
Now the final one to consider would be each box has one option. Which would be 4C1*3C1*2C1. This is my first post by the way so sorry if this is confusing.