I am not sure if this is the correct approach to these questions.
Question 3: A bag of lego containing 10 red pieces and 5 blue pieces. If you reach into the bag and pull 3 pieces
a.) How many ways have can I have all red pieces
Solution: So you have to think how many ways can I pick 3 pieces out of 15 and then how many ways can I pick all red pieces out of the 10 available.
${10\choose3} \cdot {15\choose3} $
b.) How many ways contain only 1 red piece?
Solution: So you have to think how many ways can I pick 2 blue pieces out of 15 and then how many ways can I pick 1 red piece out of the 15 available.
${10\choose1} \cdot {15\choose1} + {5\choose2} \cdot {14\choose2}$
c.) How many ways contain at least 2 or more red pieces?
Solution: So you have to think how many ways can I pick at least 2 pieces out of 15 and then how many ways can I pick at least 1 of the pieces available.
${10\choose2} \cdot {15\choose2} + {5\choose1} \cdot {13\choose1}$
a.) ${10\choose3}$ Of the 10 available red balls you want to know how many ways you can pick 3, regardless of order
b.) ${10\choose1}{5\choose2}$ Of the 10 red balls you want to choose 1 and of the 5 blue balls you want 2
c.) ${10\choose2}{5\choose1} + {10\choose3}{5\choose0}$ Of the 10 red balls you want to choose 2 and of the 5 blue balls you want 1