Hugo and viviana work in an office with ten other coworkers. out of these 12 workers, their boss needs to choose a group of five to work together on a project. suppose hugo and viviana absolutely refuse, under any circumstances, to work together. under this restriction, how many different working groups of five can be formed?

There are 252 different working groups of five that can be formed.

Step-by-step explanation:

Since we have given that

Number of workers = 12

Number of group of people to work together on a project = 5

Since  Hugo and Viviana absolutely refuse, under any circumstances, to work together.

So, remaining number of workers = 12-2=10

so, we need to find the number of different groups of five that can be formed.

We will use "Combination":

Hence, there are 252 different working groups of five that can be formed.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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