7 The 20 members of a club consist of 10 Town members and 10 Country members.
- All 20 members are arranged randomly in a straight line.
Determine the probability that the Town members and the Country members alternate.
- Ten members of the club are chosen at random.
Show that the probability that the number of Town members chosen is no more than \(r\), where \(0 \leqslant r \leqslant 10\), is given by
\(\frac { 1 } { \mathrm {~N} } \sum _ { \mathrm { i } = 0 } ^ { \mathrm { r } } \left( { } ^ { 10 } \mathrm { C } _ { \mathrm { i } } \right) ^ { 2 }\)
where \(N\) is an integer to be determined.