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As the title suggests, in how many ways can 20 identical balls be distributed in 3 identical boxes with at most 8 balls in each box and minimum 1 ball in each box ? Identical objects into distinct bins is a problem in combinatorics in which the goal is to find the number of distributions of a number of identical objects into a number of distinct bins. To find the number of ways to distribute n identical items (remaining balls) into r distinct groups (boxes), we can use the stars and bars theorem
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The formula for distributing n identical items into r distinct groups is given by: Since the balls and boxes are identical, we need to find the number of ways to distribute the balls without considering their order or the order of the boxes. In this article, we are going to learn how to calculate the number of ways in which x balls can be distributed in n boxes
This is one confusing topic which is hardly understood by students
But once mastered, it is the easiest topic of permutation and combination. In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together In this problem, we have 12 identical balls that need to be distributed into 3 identical boxes
