Having been stupid enough to open said attachment what do I find? It's not a word document its a wrapper for picture!! Grrrr...
CB
(I'm not vulnerable to macro virus's but I don't like opening word and excel attachments because it takes a long time to boot up OOO on my slow computers (I won't open an office document on the my work computers as a matter of principle)
The third part is just algebra, write out the right hand side in terms of factorials and simplify.
Alternativly one may observe that it is the sum of the number of ways of choosing a subset of elements from the given set which does not include , and the number of ways that does include .
CB
When choosing a subset consisting of elements from a set of elements the first element may be choosen in ways the second in ways and so on to the -th which may be choosen in ways. So the number of ways that the set may be choosen is , but in this number every permutation of each distinct choice appears, so to get the number of choices independent of order we divide by the number of permutations of distinct objects. Hence the number of ways of choosing the subset is:
CB
When choosing a subset consisting of elements from a set of elements the first element may be choosen in ways the second in ways and so on to the -th which may be choosen in ways. So the number of ways that the set may be choosen is , but in this number every permutation of each distinct choice appears, so to get the number of choices independent of order we divide by the number of permutations of distinct objects. Hence the number of ways of choosing the subset is:
Which is what we expect.
Now the number of ways of choosing a subset that does not contain is , and so the probability required is:
Similarly if is in the set the number of ways of choosing it is
CB