(i) To find the number of ways to choose a team of 5 from 10 people (6 boys and 4 girls) without restrictions, use the combination formula:

\(\binom{10}{5} = 252\)

(ii) To find the number of ways to choose a team with more boys than girls, consider the possible distributions:

• 5 boys and 0 girls: \(\binom{6}{5} \times \binom{4}{0} = 6 \times 1 = 6\)
• 4 boys and 1 girl: \(\binom{6}{4} \times \binom{4}{1} = 15 \times 4 = 60\)
• 3 boys and 2 girls: \(\binom{6}{3} \times \binom{4}{2} = 20 \times 6 = 120\)

Summing these, the total number of ways is:

\(6 + 60 + 120 = 186\)