They have changed the rules for resolution passage within the UN Security Council. It still takes all 5 permanent members to vote “for” a resolution, but it will now take a total of 11 “for” votes to pass. How many ways can a resolution pass?

It depends on how many members there are in the council. If there are only 11, then only a unanimous vote will do.

If there are N members, then at least 6 of the N-5 members will need to vote yes.

There are 10 non-permanent and 5 permanent members for a total of 15.

This means that there must be at least n votes from the 10 non-permanent members, where n≥6.

So the number of ways the votes can go are:
C(10,6)+C(10,7)+C(10,8)+C(10,9)+C(10,10)
=386
where C(10,6)=10!/(6!(10-6))
(check my arithmetic).

To determine how many ways a resolution can pass under the new rules, we need to consider the number of possible combinations of member votes.

Under the new rules, it requires all 5 permanent members to vote "for" a resolution, so we need to consider the remaining 6 non-permanent members. Out of these 6 members, we need to select additional votes until we reach a total of 11 "for" votes.

To calculate this, we can use the concept of combinations. The formula for combinations is:

C(n, r) = n! / (r! * (n-r)!)

Where:
- n is the total number of options available (in this case, the number of non-permanent members, which is 6)
- r is the number of options we want to select (in this case, the number of additional "for" votes needed to reach a total of 11, which is 11-5=6)

So, the number of ways a resolution can pass under the new rules is:

C(6, 6) = 6! / (6! * (6-6)!) = 6! / (6! * 0!) = 6! / 6! = 1

Therefore, there is only 1 way for a resolution to pass under the new rules.