Answer: (a) \(98\); (b)(i) \(60480\); (b)(ii) \(720\).

Answer: (a) \(98\); (b)(i) \(60480\); (b)(ii) \(720\).

(a) There are two allowed cases.

If both sisters are chosen, the other \(4\) people are chosen from the remaining \(8\) people:

\(\binom84=70.\)

If neither sister is chosen, all \(6\) people are chosen from the remaining \(8\) people:

\(\binom86=28.\)

So the total number of teams is

\(70+28=98.\)

(b)(i) There are \(9\) different characters and \(6\) positions, with no repetition. Hence the number of passwords is

\(^9P_6=9\times8\times7\times6\times5\times4=60480.\)

(b)(ii) The first two positions must be letters. They can be arranged in

\(^3P_2=6\)

ways. The last two positions must be digits, also in

\(^3P_2=6\)

ways. After that, \(5\) characters remain for the two middle positions, so there are

\(^5P_2=20\)

ways to fill them. Therefore the number of passwords is

\(6\times6\times20=720.\)