以下有幾條nPr和nCr的問題

1. An examination paper has 3 sections A,B and C.A student must do 4 out of 7 questions in section A,3 out of 5 questions in section B and 2 out of 3 questions in section C.In how many different ways can a student attempt the paper?

2. A student has 15 different books.In how many ways can he arrange 12 of them on a shelf if
a) there is no restriction
b) a particular book must be on a shelf
c) 2 particular books must be on the shelf and placed together

3. 8 out of 12 scouts are selected to stand half on each side of a hall entrance.Find the number of ways in which this may be done if
a) there is no restriction
b) the 2 tallest scouts must stand at the end of each side

4. 5 identical Toyota and 2 identical Honda cars are parked in a row.Find the number of different arrangements if there is no restrictions?

5. Susan decorates her christmas tree using a series of light bulbs.She has 5 red,4 yellow and 2 blue bulbs available.
a) If she uses all the light bulbs,how many different arrangement can she make?
b) In a) , how many of the arrangements will the two blue bulbs be separated?