A lacrosse team is selecting a captain. The names of all the seniors are put into a hat, and the first three that are drawn will be the captains. The names are not replaced once they are drawn (one person cannot be two captains). You want to see if the captains all play the same position. State whether this is binomial or not and state why.

In statistics, binomial distribution for a discrete random variables with two possible outcomes. A random variable is said to have a binomial distribution if the probability mass function is:

$P(X=x)=\frac{n!}{(n-x)!x!}{p}^x{(1-p)}^{n-x}$

The probability distribution of binomial distribution has two parameters $n=numberoftrials$and $p=numberofsuccess.$.The binomial distribution is of the form:

$X~B(n,p)$

The requirements for a distribution to be a binomial distribution are as follows:

1. There are a set number of trials, n,
2. The n trials are independent and are conducted under the same conditions each time.
3. The trials can only result in one of two outcomes: "success" or "failure."
4. On one trial, p denotes the probability of success and q is the probability of failure.

When we examine the presented experiment, we can see that the names are not replaced once they have been drawn. As a result, the chances of winning in each draw and event would not be independent.