Identify the initial amount a and the growth factor b in the exponential function. a(x)=680*4.3^x

The number of outcomes in M is 24, each one with a probability to happen. The probability of M to happen is

Step-by-step explanation:

There are 4 people and 4 different pairs of socks which we will denote by A,B,C and D. If every person ends with a matching pair of socks that means that:

Person 1 ended with pair A,B,C or D. (4 possibilities).Person 2 ended with pair A,B,C or D, but without the pair that Person 1 has. (3 possibilities).Person 3 ended with pair A,B,C or D, but no with the pair person 1 has neither the one of person 2 has. (2 possibilities).Person 4 will end with the remaining pair of socks (1 possibility).

Therefore the numbers of outcomes of M is

It is clear that each one of those outcomes have the same probability to happen. Then we will compute the probability of one of them (which we will denote as ) and then multiply by 24 to obtain the probability of M.

We will compute the probability of:

Person 1 choosing pair A={1,2}Person 2 choosing pair B={3,4}Person 3 choosing pair C={5,6}Person 4 choosing pair D={7,8}

Without loss of generality we will assume that person 1 chooses first, then person 2 and so on.

Observe that the number of ways of choosing 2 socks is given by:

Therefore, the probability of person 1 to choose the pair A={1,2} is .

After that, there would remain 6 socks in the bag. Then, the probability of person 2 of choosing pair B={3,4} is 1 in . That is

After that, there would remain 4 socks in the bag. Then, the probability of person 3 of choosing pair C={5,6} is 1 in . That is

Finally when person 4 chooses, there would be only 2 socks (pair D={7,8}) so, the probability of choosing pair D is 1.

Therefore, the probability of to happen is

And in consequence