9) A box contains 10 different colored light bulbs. Find the number of ordered samples of size 3 with replacement.
10^3
Ah, lightbulbs, one of the brightest topics indeed! To find the number of ordered samples of size 3 with replacement from a box of 10 different colored lightbulbs, we can think of it as a dazzling mathematical dance routine.
Now, imagine each lightbulb has its own unique style. They're all lined up backstage, eagerly waiting for their turn in the spotlight. Since we're allowing replacement, it means after each selection, the lightbulb goes back to the line to be chosen again.
To determine the number of ordered samples, we can use a simple formula. It's like putting a bulb in a high-pressure immersive environment, but without the popping sound – trust me, it's a lot less dangerous!
The formula is the art of multiplication, my friend. We take the number of options for each bulb and raise it to the power of the sample size. In this case, with 10 dazzling bulbs dance freely in our box and a sample size of 3, we have:
10^3 = 1000
Voila! We have a thousand possibilities to create gloriously ordered samples of size 3 with replacement from the box of 10 different colored lightbulbs. Now that's thinking bright!
To find the number of ordered samples of size 3 with replacement from a box containing 10 different colored light bulbs, we can use the formula for permutations with replacement.
The formula for permutations with replacement is given by n^r, where n is the number of options for each sample and r is the size of the sample.
Here, n = 10, as there are 10 different colored light bulbs, and r = 3, as we are selecting a sample of size 3.
Using the formula, the number of ordered samples of size 3 with replacement would be:
10^3 = 1000
Therefore, there are 1000 different ordered samples of size 3 with replacement from the box containing 10 different colored light bulbs.
To find the number of ordered samples of size 3 with replacement from a box containing 10 different colored light bulbs, we can use the concept of permutations.
With replacement means that after each selection, we put the light bulb back in the box, so it can be selected again.
To calculate the number of ordered samples with replacement, we can use the formula:
N^r
Where N is the total number of objects in the box (10 in this case) and r is the size of the sample (3 in this case).
So, in this case, the number of ordered samples with replacement would be:
10^3 = 1000
Therefore, there are 1000 different possible ordered samples of size 3 that can be selected with replacement from a box containing 10 different colored light bulbs.