<h3>
Answer: 10,080</h3>
Explanation:
There are 8 letters so there are 8! = 8*7*6*5*4*3*2*1 = 40,320 permutations of those letters. However, the letters "O" and "L" show up twice each, so we must divide by 2! = 2*1 = 2 for each instance this happens.
So,
(8!)/(2!*2!) = (40,320)/(2*2) = (40,320)/4 = 10,080
is the number of ways to arrange the letters of "football".
The reason we divide by 2 for each instance of a duplicate letter is because we can't tell the difference between the two "O"s or the two "L"s. If there was a way to distinguish between them, then we wouldnt have to divide by 2.
(-2/3) / (5/4) =
-2/3 * 4/5 =
-8/15 <=
Answer:
a)
And then we have our probability distribution like this:
X | 0 | 1 | 2 |
P(X) | 0.7921 | 0.1958 | 0.0121|
b) 
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:

Solution for the problem
Part a
On this case since we select a sample size of n =2 we have the following values for the number of left handed X=0,1,2. We can find the probabilities for each case since we know that p=0.11.
And then we have our probability distribution like this:
X | 0 | 1 | 2 |
P(X) | 0.7921 | 0.1958 | 0.0121|
Part b
For this case we want this probability:

Answer:
I think that the ratio would be 12:11
Step-by-step explanation:
Because if you multiply 3 and 9 then you do 12:11