Ways to Arrange Balls Problem

You are given 'a' balls of type 'A', 'b' balls of type 'B', and 'c' balls of type 'C'. Determine the total number of ways to arrange these balls in a straight line so that no two adjacent balls are of the same type.

Input:

The first line of input consists of an integer 'T', which represents the number of test cases. For each test case, there is a single line containing three space-separated positive integers: a, b, c.

Output:

For each test case, output a single integer denoting the total number of valid arrangements of balls where no two adjacent balls are of the same type.

Example:

Input:

2 2 1 1 1 0 1

Output:

6 0

Explanation:

For the first test case, there are 6 ways to arrange: ABCA, ABAC, ACBA, ACAB, BACA, CABA.
For the second test case, there is no valid arrangement, hence the output is 0.

Constraints:

1 ≤ T ≤ 100

0 ≤ a, b, c ≤ 15

Time limit: 1 sec

Question

Ways to Arrange Balls Problem

You are given 'a' balls of type 'A', 'b' balls of type 'B', and 'c' balls of type 'C'. Determine the total number of ways to arrange these balls in a straight line so that no two adjacent balls are of the same type.

Input:

The first line of input consists of an integer 'T', which represents the number of test cases.
 For each test case, there is a single line containing three space-separated positive integers: a, b, c.

Output:

For each test case, output a single integer denoting the total number of valid arrangements of balls where no two adjacent balls are of the same type.

Example:

Input:

2
2 1 1
1 0 1

Output:

6
0

Explanation:

For the first test case, there are 6 ways to arrange: ABCA, ABAC, ACBA, ACAB, BACA, CABA.
For the second test case, there is no valid arrangement, hence the output is 0.

Constraints:

1 ≤ T ≤ 100
0 ≤ a, b, c ≤ 15
Time limit: 1 sec

Accepted Answer

The problem involves arranging balls of different types in a straight line without having two adjacent balls of the same type.

Use recursion to try all possible arrangements while keeping track of the previous ball type.
Handle edge cases where one or more types of balls have a count of 0.
Consider using dynamic programming to optimize the solution by storing intermediate results.
For the given example input (2 1 1), the output is 6 as there are 6 valid arrangements.
For the input (1 0 1), the output is 0 as there is no valid arrangement possible.