Can somebody explain the following problem?
Suppose you have an urn (a bucket) with 10 green balls and 7 red balls.
(a) Suppose you draw 8 balls out of the bucket all at once. How many ways are there to draw 4 red balls and 4 green ones?
(b) Imagine that the balls are numbered 1 through 17. Suppose you draw 3 balls out of the bucket one at a time with replacement after each draw. How many ways are there to draw exactly 2 red balls? (Hint: for each draw there are exactly 7 ways to draw a red and 10 ways to draw a green).
(c) Suppose you draw 10 balls out of the bucket without replacement. How many ways are there to draw exactly 4 red and 6 green balls? (Hint: count by first determining how many ways you can place 4 red balls among 10 positions, then determine how many ways there are to rearrange the red balls and how many ways you can rearrange the green balls)
My solutions so far:
a) 7 choose 4 (number of ways to draw 4 red balls) * 10 choose 4 (number of ways to draw 4 green balls)= 7350 ways
b) I don't understand if order matters or not. If order does not matter then C(3,2)*7^2*10^1
c) C(10,4)*C(10,6)= C(10,4)^2
Suppose you have an urn (a bucket) with 10 green balls and 7 red balls.
(a) Suppose you draw 8 balls out of the bucket all at once. How many ways are there to draw 4 red balls and 4 green ones?
(b) Imagine that the balls are numbered 1 through 17. Suppose you draw 3 balls out of the bucket one at a time with replacement after each draw. How many ways are there to draw exactly 2 red balls? (Hint: for each draw there are exactly 7 ways to draw a red and 10 ways to draw a green).
(c) Suppose you draw 10 balls out of the bucket without replacement. How many ways are there to draw exactly 4 red and 6 green balls? (Hint: count by first determining how many ways you can place 4 red balls among 10 positions, then determine how many ways there are to rearrange the red balls and how many ways you can rearrange the green balls)
My solutions so far:
a) 7 choose 4 (number of ways to draw 4 red balls) * 10 choose 4 (number of ways to draw 4 green balls)= 7350 ways
b) I don't understand if order matters or not. If order does not matter then C(3,2)*7^2*10^1
c) C(10,4)*C(10,6)= C(10,4)^2