Problem Solving

Can someone explain to me the answers for the following 3 questions on GMAT prep exam. Thanks!

1. A certain law firm consists of 4 senior partners and 6 junior partners. How many different groups of 3 partners can be performed in which at least one member of the group is a senior partner? (Two groups are considered different if at least one group member is different)
a) 48
b) 100
c) 120
d) 288
e) 600
the answer is B, but i don't understand how.

2. A certain Basket contains 10 apples, 7 of which are red and 3 of wich are green. If 3 different apples are to be selected at random from the basket , what is the probability that 2 of the apples selected will be red and 1 will be green?
a) 7/40
b) 7/20
c) 49/100
d) 21/40
e) 7/10
the answer is D, again i would like to get an explaination how

3. In a class of 30 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest of the students each borrowed at least 3 books. If the average (arithmetic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed ?
a) 3
b) 5
c) 8
d) 13
e) 15
the answer is D, but don't understand how

Atleast 1 senior(S) means one or more

1. No of ways of selecting the group with 1S and 2J= 4C1*6C2
2.with 2S and 1J= 4C2*6C1
3.with 3S and 0J=4C3*6C0

Total no of ways= 60+36+4=100

[u]Second problem[/u]

Probability that E occurs =No of favourable events for E/Total no of events

No of ways of selecting green apple from 3 greens * No of ways os selecting 2 red apples from reds/ total no of ways of selecting 3 apples from 10


7C2*3C1/10C3 =21/40

[u]Third Problem[/u]


Mean= 2(0)+12(1)+10(2)+6(x)/30

6 being the remaining who were allowed to borrow atleast 3. To know the max books a single student could borrow… we must restrict the other five among these 6 remaining students to 3 books (the min)

2(30)=32+5(3)+x
X=13

People please do follow the rule of one question per thread ..