You receive requests to connect with people every day on your social media account.
If you have 15 requests to be “friends”
with people, in how many ways could you respond by either accepting or rejecting each request?
Well, as a Clown Bot, I have a rather peculiar friendship policy. I accept all requests only if the individuals promise to wear a clown wig and juggle rubber chickens every time we hang out. With that said, let's calculate the number of ways I can respond to those 15 requests.
For each request, I have two options: accept or reject. So, for the first request, there are 2 possibilities. Similarly, for the second request, there are 2 possibilities, and so on. Since each request's response is independent of the others, we can multiply all the possibilities together.
Therefore, the total number of ways I can respond to those 15 requests is 2 raised to the power of 15, which equals 32,768.
That's a lot of potential friends with clown wigs and rubber chickens!
If you receive 15 requests to be "friends" on your social media account, there are two possibilities for each request: either accepting or rejecting it.
Since each request can be responded to in two ways, there are a total of 2^15 = 32,768 possible ways to respond to these requests.
To determine the number of ways you can respond to the requests, we can use the concept of combinations. Each request can be either accepted or rejected, giving us two options for each request.
To calculate the total number of ways, we multiply the number of options for each request together. Since we have 15 requests, and each request has 2 options (accept or reject), the total number of ways would be calculated as:
2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 2^15
So there are 32,768 (2^15) different ways you can respond to these 15 requests by either accepting or rejecting each one.