Question

Consider a three-dimensional grid whose dimensions are 10 by 15 by 20. you are at the front lower left corner of the grid and wish to get to the back upper right corner 45 "blocks" away. how many different routes are there in which you walk exactly 45 blocks?

Answer 1

To find the number of different routes in which you walk exactly 45 blocks in a 3D grid, you can use the concept of combinations. Calculate the number of different routes by substituting the values into the combination formula. Simplify the equation to find the value.

Step-by-step explanation:

To find the number of different routes in which you walk exactly 45 blocks to get from the front lower left corner to the back upper right corner, you can use the concept of combinations. Since you are allowed to move only east, north, or up, the number of blocks you move in each direction is fixed. In this case, you would move 10 blocks east, 15 blocks north, and 20 blocks up. To calculate the number of routes, you can use the formula for combinations:

C(n, r) = n! / (r!(n-r)!)

In this case, n = 45 (the total number of blocks you need to move), r1 = 10 (the number of blocks east), r2 = 15 (the number of blocks north), and r3 = 20 (the number of blocks up). Substituting these values into the formula, you get:

C(45, 10) * C(35, 15) * C(20, 20) = 45! / (10!(45-10)!) * 35! / (15!(35-15)!) * 20! / (20!(20-20)!)

After simplifying the equation, you can calculate the value to find the number of different routes.

Answer 2

45 steps there will be 10 steps to the right then 15 steps up and 20 steps forward. It is just like counting sequences of 45 letters. so 10 is R then 15 U, is and 20 is F. ending the multinomial coefficient

( 45 )
10, 15, 20 = 45/101520 or 45 over 10 15 20