I make it about 780 million to one against the all eleven cards will be of a particular suit. The way I work this out is that the probability that the first card will be of a particular suit is 13 in 52, or 1 in 4, which can be represented as 0.25. On the second card the probablility is 12 in 51, or .235; and so on until before dealing the 11th card the probability will be 3 in 42 or .071. You then multiply together all these probability fractions, which gives you 1282357 with 8 noughts in front; then by dividing this fraction into one, you get the figure of 779,814,045, gives you the odds against it all happening.
Now someone, tell me where I went wrong!