Question

The number of ways to distribute 30 identical candies among four children c1 , c2 , c3 and c4 so that c2 receives atleast 4 and atmost 7 candies, c3 receives atleast 2 and atmost 6 candies, is equal to

a. 205
b. 615
c. 510
d. 430

Answer 1

The number of ways to distribute 30 identical candies among four children with certain restrictions can be found using the concept of stars and bars. The number of ways is 910.

Step-by-step explanation:

To find the number of ways to distribute 30 identical candies among four children, we can use the concept of stars and bars. Let's consider the restrictions for each child.

c2: At least 4 and at most 7 candies

c3: At least 2 and at most 6 candies

First, we will distribute the minimum candies required for c2 (4) and c3 (2). This leaves us with 30 - 4 - 2 = 24 candies to distribute among four children.

Next, we will distribute the remaining candies among the four children. We can think of it as finding the number of ways to distribute 24 candies among four children, with no restrictions.

The number of ways to distribute 24 candies among four children is given by the formula (24+4-1)C(4-1), where C represents combination.

Therefore, the number of ways to distribute the candies is (24+4-1)C(4-1) = 27C3 = 27!/3!(27-3)! = 27*26*25/3*2*1 = 910 ways.