Mastering Combinations: Calculate Unique Meetings for Six Sigma Black Belts

How many unique meetings consisting of one black belt and two quality engineers can be formed from five black belts and eight quality engineers?

• A. 40
• B. 80
• C. 140
• D. 280

Answer: (C)

To determine how many unique meetings can be formed with one black belt and two quality engineers from five black belts and eight quality engineers, we need to utilize combinations. First, we consider the selection of one black belt. Since there are five black belts available, the number of ways to choose one black belt can be calculated using combinations. This is given by: C(5, 1) = 5 Next, we need to select two quality engineers from the eight available. The number of ways to choose two quality engineers can also be calculated using the combinations formula: C(8, 2) = 8! / (2!(8-2)!) = 8! / (2! * 6!) = (8 * 7) / (2 * 1) = 28 To find the total number of unique meetings, we multiply the number of ways to choose the black belt by the number of ways to choose the quality engineers: Total unique meetings = C(5, 1) * C(8, 2) = 5 * 28 = 140 Thus, the correct answer is 140, indicating that it's possible to create 140 distinct combinations of one black belt and two quality

When it comes to preparing for the Six Sigma Black Belt certification, understanding how to tackle problems related to combinations can be a game-changer. You might think, "Combinations? Why does that even matter?" Well, let’s explore this together, especially if you're looking to ace your practice exam!

Picture this: You've got five black belts and eight quality engineers. You're tasked with forming a meeting that includes one black belt and two quality engineers. How many unique ways can you pull this off? That might sound a bit confusing at first, but it's actually a classic combinations problem that can boost your confidence!

To start, let's focus on those black belts. We need to choose one out of the five available options. The beauty of combinations is that we can calculate this using a straightforward formula. Here’s the essential calculation:

Choosing one black belt:

Parameters: C(5, 1) = 5

This means there are five different ways to choose one black belt. Easy, right?

Now, the next step involves the quality engineers. We need to select two from the eight available. Hold onto your hats; this is where it gets a little more interesting! We’ll also use the combinations formula for this one:

Choosing two quality engineers:

C(8, 2) = 8! / (2!(8-2)!)

= 8! / (2! * 6!)

= (8 * 7) / (2 * 1)

= 28

Did you catch that? There are 28 unique ways to choose two quality engineers from the group.

Now, to find the total number of unique meetings we can form, it's simply a matter of multiplication. Let's stitch these parts together!

Total unique meetings:

C(5, 1) * C(8, 2) = 5 * 28 = 140

So, the verdict? You can form 140 unique meetings with the given parameters. And now you know why understanding combinations is essential when you're preparing for your Six Sigma certification. Whether you're actually practicing these calculations or just getting your mind in gear, it’s a skill you want in your toolkit.

And here’s the thing – this little exercise not only strengthens your problem-solving skills, but it also sharpens your analytical thinking, both of which are crucial for the Six Sigma methodologies. Perhaps, while you’re at it, think about other scenarios where combinations can unravel new paths. From project planning to resource allocation, the possibilities are endless!

By now, you should feel more comfortable tackling similar problems, and remember, practice makes perfect. Get those numbers flowing, and before you know it, you’ll be on your way to proudly displaying that Black Belt certification. Keep this knowledge fresh as you prepare, and don’t hesitate to revisit strategies like combinations whenever you can. It's all part of the journey in mastering Six Sigma!