Originally Posted by

**mr fantastic** I'm not sure this answer is correct since it doesn't work for n = 3 .....

Let the names of the people be A, B and C and A is the host.

There are only two possible distributions:

A, B, C

C, A, B with probability 1/2. Number of names not called out = 0.

B, C, A with probability 1/2. Number of names not called out = 0.

Therefore expected value of names not called out = (0)(1/2) + (0)(1/2) = 0. Yet the proposed answer gives (3/2) - 1 = 1/2 ......

I don't have time right now to look more closely (not one word from anyone .........) but will try to later.