form 6 Permutaion and Combination, please help!

1. A class has a total of 20 students of which five are male.
If three students are chosen, in how many ways can at least
2 of the 3 are male students?
Sol:
2 male students ~
C153 × C52
＝ 455 * 10
＝ 4550
3 male student
C152 × C53
＝ 105 × 10
＝ 1050
4550 ＋ 1050
＝ 5600
Ans: 5600 ways
2. A team of 3 students are to be selected from a group of
4 boys and 5 girls to participate in a debate
( a ) How many different teams of three can be formed?
( b ) In how many ways that the team consists of exactly
one boy and two girls?
Sol:
( a )
C93 × C63 × C33 ÷ 3!
＝ 84 × 20 × 1 ÷ 6
＝ 280
( b )
(C31×C62) × (C21×C42) × (C11×C22) ÷ 3!
＝ (3*15) × (2*6) × (1*1) ÷ 6
＝ 45 × 12 × 1 ÷ 6
＝ 90
Ans: ( a ) 280 ways ( b ) 90 ways
Send me a letter and tell me which step if you don’t understand.

1. 5600 ways

2. ( a ) 280 ways ( b ) 90 ways