(a) How many ways are there to put twelve identical balls into four boxes numbered 1, 2, 3, and 4?
(b) How many ways are there to put n identical balls into k boxes numbered 1, 2, . . ., k?
(a) How many ways are there to put twelve identical balls into four boxes numbered 1,...
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6 red boxes labelled 1 to 6 and 6 blue boxes labelled 1 to 6, such that the blue be with label i and the red box with labeli receive the same number of balls, for every ie (1,2,3,4,5, 6}? [10 marks
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6 red boxes labelled 1 to 6 and...
3. (a) (3 pts.) Determine in how many ways one can place twelve indistinguishable balls in six boxes in such a way that none of the boxes is empty. (b) (3 pts.) Repeat the exercise from part (a) with r balls and n boxes, where r > n.
3. (a) (3 pts.) Determine in how many ways one can place twelve indistinguishable balls in six boxes in such a way that none of the boxes is empty. (b) (3 pts.) Repeat the exercise from part (a) with r balls and n boxes, where r>n
In how many ways can n identical balls be distributed into k bins such that each bin contains at least two balls. Assume that n ≥ 2k.
How many ways can four red balls and four blue balls be randomly placed in eight urns that are numbered one to eight so that exactly one ball is in each urn?
How many ways can n identical balls be distributed into k bins such that each bin contains at least two balls? Assume that n ≥ 2k. Please type your answer or use neat handwriting.
We randomly distribute 5 identical balls to 3 distinct boxes numbered 1,2,3. Given that no box is empty find the probability that box 1 contains 3 balls.
3. An urn contains five white balls numbered from 1 to 5, five red balls numbered from 1 to 5 and five blue balls numbered from 1 to 5. For each of the following questions, please give your answer first in the form that reflects your counting process, and then simplify that to a number. You must include the recipes. No other explanation needed. (a) In how many ways can we choose 4 balls from the urn? (b) in how...
4. A box contains N identical balls numbered 1 through N. Of these balls, n are drawn at -1 Xi a time. Let Xi , X2,···x, denote the numbers on the n balls drawn. Let S,- Find var(S)
1.23 A box contains n identical balls numbered 1 through n [Papoulis 1.1]. Suppose k balls are drawn in succession. a) what is the probability that m is the largest number drawn? b) what is the provability that the largest number drawn is less than or equal to m?