In statistics, random samples are used to make generalizations, or inferences, about a population. Give a full correct answer for this question its true or false?

In how many ways can 7 graduate students be assigned to 1 triple and 2 double hotel rooms during a conference

Solve the following problems applying Polya’s Four-Step Problem-Solving strategy.
If six people greet each other at a meeting by shaking hands with one another, how many handshakes take place?

A simple random sample of 1,000 United States adults was collected to investigate whether gender and being a coffee drinker are independent. The results are summarized in the table with the expected counts shown in parentheses.
$\begin{array}{cc}& \text{ Coffe Drinker? }\\ \text{Gender}& \begin{array}{|cccc|}\hline & \text{ Yes }& \text{ No }& \text{ Total }\\ \text{ Male }& 191(148.5)& 299(341.5)& 490\\ \text{ Female }& 112(154.5)& 398(355.5)& 510\\ \text{ Total }& 303& 697& 1,000\\ \hline\end{array}\end{array}$
Which statement is true about whether the conditions for the chi-square test for independence have been met?
a. All necessary conditions are satisfied to apply a chi-square test for independence between gender and being a coffee drinker.
b. The data is not the result of two independent random samples; therefore, the conditions for applying the chi-square test for independence between gender and being a coffee drinker are not met.
c. Not all of the expected cell counts are large enough to satisfy the conditions for applying the chi-square test for independence between gender and being a coffee drinker.
d. Not all of the observed cell counts are large enough to satisfy the conditions for applying the chi-square test for independence between gender and being a coffee drinker.
e. The total sample size is not at least 10 percent of the population of United States adults; therefore, the conditions for applying the chi-square test for independence between gender and being a coffee drinker are not met.

A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 536 randomly selected Americans surveyed, 441 were in favor of the initiative. Round answers to 4 decimal places where possible. a. With 90% confidence the proportion of all Americans who favor the new Green initiative is between and . b. If many groups of 536 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about percent will not contain the true population proportion.

How does fire spread on a piece of paper?
If one lights the corner of a piece of paper with a match, the fire gradually spreads. What equation can be used to predict how the fire is going to spread spatially and temporally? At first, I thought thermodynamics would give answer to this question. But as far as I know, thermodynamics does not say anything about the dynamics of a system. So, how to tackle this question?

Suppose we are testing 20 drugs and use a significance value of 0.01 in each test. Suppose at least one out of the 20 tests rejects the null hypothesis. What is the upper bound for the probability that declaring the corresponding drug useful is a type I error (i.e. reject null hypothesis when one should not)?
I am confused on where to start. Any help is appreciated