My school's math club has 6 boys and 8 girls. I need to select a team to send to the state math competition. We want 6 people on the team. In how many ways

My school's math club has 6 boys and 8 girls. I need to select a team to send to the state math competition. We want 6 people on the team. In how many ways can I select the team to have more girls than boys?

0 boys,  6 girls           1*8C6   ways

1 boy     5 girls           6*8C5    ways

2 boys    4 girls           6C2 * 8C4   ways

add those altogether :)

1*8C6 = 28

6*8C5 = 336

6C2*8C4 = 15*70 = 1050

1050 + 336 + 28 = 1414