6 A bag contains 6 identical blue counters and 5 identical yellow counters.
- Three counters are selected at random, without replacement.
Find the probability that at least two of the counters are blue.
All 11 counters are now arranged in a row in a random order.
- Find the probability that all the yellow counters are next to each other.
- Find the probability that no yellow counter is next to another yellow counter.
- Find the probability that the counters are arranged in such a way that both of the following conditions hold.
- Exactly three of the yellow counters are next to one another.
- Neither of the other two yellow counters is next to a yellow counter.
- Explain whether the answer to part (d) would be different if the yellow counters were numbered \(1,2,3,4\) and 5 , so that they are not identical.