In a coordinate system, A is the origin and B is the point (15, 8). One has to go from A to B, taking steps only rightwards or upwards. If each rightward step is 3 units long and each upward step is 2 units long, in how many ways can one go from A to B?

This problem can be solved using the concept of permutations and combinations.

Step 1: Determine the total number of steps required in each direction. To reach the point B(15, 8) from the origin A(0, 0), one needs to move 15 units to the right and 8 units up. Since each rightward step is 3 units long, the total number of rightward steps required is 15/3 = 5. Similarly, since each upward step is 2 units long, the total number of upward steps required is 8/2 = 4.

Step 2: Calculate the total number of steps. The total number of steps required to reach from A to B is the sum of the number of rightward and upward steps, which is 5 + 4 = 9.

Step 3: Use the formula for combinations to calculate the number of ways. The number of ways to go from A to B is given by the combination of the total number of steps taken 9, taken 5 at a time (the number of rightward steps). This is because out of the 9 steps, we choose 5 steps to be in the rightward direction (or equivalently, we could choose 4 steps to be in the upward direction).

The formula for combinations is C(n, r) = n! / [(n-r)! * r!], where n is the total number of items, r is the number of items to choose, and '!' denotes factorial.

Step 4: Substitute the values into the formula. C(9, 5) = 9! / [(9-5)! * 5!] = 9! / (4! * 5!) = 126

So, there are 126 ways to go from point A to point B, taking steps only rightwards or upwards.