# Thread: Basics Of Counting - Total number of strings

1. ## Basics Of Counting - Total number of strings

Hello! So I'm doing a basics of counting and just need some help with these questions and determining wether my logic is flawed:

Suppose Bob wants to apply two modifications to produce a string like9Super5man or a string like Super95man. We want to determine the differentstrings Bob can create. He does this in two steps:

Step 1. Choose the first number (say 5) and insert it in Superman. (Itproduces Super5man, etc.)

Step 2. Choose the second number (say 9) and insert it in the stringobtained after Step 1. (If the string from step 1 was Super5man, then theresult can be 9Super5man or Super95man, etc.)

b2. To determine the number of different strings Bob can create, we canjust apply the Product Rule. Explain why the product1rule will result in overcounting. In particular, what strings will be countedmore than once?

So i'm a bit off complete lost here. I'm not sure how you would use the product rule in this case. It would be overcounting because 95superman and 59superman would both be counted? I can't understand if that is what the question would consider overcounting.

b3. How would you solve the problem? Explain why you think it is correct.

_ _ s _ _ u _ _ p_ _ e_ _ r_ _ m_ _a_ _ n_ _

Would this be correct: 20 --> total number of positions 10 ----> total number of digit options

So: (20 x 10) (first option) + (20 x 10) (second option)

2. ## Re: Basics Of Counting - Total number of strings

Originally Posted by elitetiger
Suppose Bob wants to apply two modifications to produce a string like9Super5man or a string like Super95man. We want to determine the differentstrings Bob can create. He does this in two steps:

Step 1. Choose the first number (say 5) and insert it in Superman. (Itproduces Super5man, etc.)

Step 2. Choose the second number (say 9) and insert it in the stringobtained after Step 1. (If the string from step 1 was Super5man, then theresult can be 9Super5man or Super95man, etc.)

b2. To determine the number of different strings Bob can create, we canjust apply the Product Rule. Explain why the product1rule will result in overcounting. In particular, what strings will be countedmore than once?
@elitetiger, do you know how to use a space bar on a keyboard? If so why don't you above?

$\underbrace {\_\_}_{1}S\underbrace {\_\_}_{2}U\underbrace {\_\_}_{3}P\underbrace {\_\_}_{4}E\underbrace {\_\_}_{5}R\underbrace {\_\_}_{6}M\underbrace {\_\_}_{7}A\underbrace {\_\_}_{8}N\underbrace {\_\_}_{9}$
So you have nine places to put the $9$.

Say you do this: $\underbrace {\_\_}_{1}S\underbrace {\_\_}_{2}U\underbrace {\_\_}_{3}P\underbrace {\_\_}_{4}E\underbrace {\_\_}_{5}R\underbrace {\_\_}_{6}M\underbrace {\_\_}_{7}A\underbrace {\_\_}_{8}9\underbrace {\_\_}_{9}N\underbrace {\_\_}_{10}$
Now you have ten places to place the five. So that is ninety places in all.

That is what you wrote. If it is not what you meant, try again to rewrite the post.