There are 9 jars each with unique labels.
Someone has come and removed all the labels and mixed them up.
If you put the labels back on the jars (without knowing the contents), what is the expected number of labels which would match the contents?
If there were only 1 jar, you'd expect it to get the correct label. Expected correct labels: 1
If there were two jars, there's a fifty-fifty shot of getting them both right or both wrong. Expected correct labels = 1/2 x 0 + 1/2 x 2 = 1
If there were three jars, you have a 1/3 chance of getting the label on the first jar right. If this happens, there's a fifty-fifty shot as above. If the first label is wrong, then it's a fifty-fifty shot of getting either just one of the remaining labels right, or getting neither of them right. Expected correct labels = 1/3 x (1 + 1) + 2/3 x (0 + 1/2) = 1.
Nothing formal here, but it looks like the expected result is 1 correct label regardless of the number of cans.
A pattern
