91Ó°ÊÓ

A restaurant offers six choices for the main dish. How many ways can a group of nine women select the main dish? Assume that order does not matter.

Solve each equation, where \(n \geq 0\). $$C(n, n-2)=55$$

The nth Fibonacci number \(F_{n}\) is given by the sum of the numbers along the \(n\) h northeast diagonal of Pascal's triangle; that is, $$ F_{n}=\sum_{i=0}^{\lfloor(n-1) / 2\rfloor}\left(\begin{array}{c}{n-i-1} \\\ {i}\end{array}\right) $$ Using this formula, compute each Fibonacci number. $$ F_{2} $$

Using the recursive definition of \(b_{n},\) compute each. $$b_{8}$$

An old zip code in the United States consists of five digits. Find the total number of possible zip codes that: Have no repetitions.

Five marbles are selected at random from a bag of seven white and six red marbles. Find the probability of each event. Two are white and three are green.

The \(n\) th Fibonacci number \(F_{n}\) is given by the sum of the numbers along the \(n\) th northeast diagonal of Pascal's triangle; that is, $$F_{n}=\sum_{i=0}^{\lfloor(n-1) / 2\rfloor}\left(\begin{array}{c} n-i-1 \\ i \end{array}\right)$$ Using this formula, compute each Fibonacci number. $$F_{2}$$

In how many ways can 10 quarters in a piggy bank be distributed among 7 people?

Find the number of ways of dividing a set of size \(n\) into two disjoint subsets of sizes \(r\) and \(n-r\).

Let \(U=|\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}|\) be the sample space of an experiment, where the outcomes are equally likely. Find the probability of each event. $$\\{a\\}$$