91Ó°ÊÓ

Solve each problem involving combinations. A city council is composed of 5 liberals and 4 conservatives. Three members are to be selected randomly as delegates to a convention. (a) How many delegations are possible? (b) How many delegations could have all liberals? (c) How many delegations could have 2 liberals and 1 conservative? (d) If 1 member of the council serves as mayor, how many delegations are possible that include the mayor?

Evaluate the terms of \(\sum_{i=1}^{4} f\left(x_{i}\right) \Delta x,\) with \(x_{1}=0, x_{2}=2, x_{3}=4, x_{4}=6,\) and \(\Delta x=0.5,\) for each function. $$f(x)=\frac{-2}{x+1}$$

Use a formula to find the sum of each arithmetic series. $$89+84+79+74+\cdots+9+4$$

Evaluate the terms of \(\sum_{i=1}^{4} f\left(x_{i}\right) \Delta x,\) with \(x_{1}=0, x_{2}=2, x_{3}=4, x_{4}=6,\) and \(\Delta x=0.5,\) for each function. $$f(x)=\frac{5}{2 x-1}$$

Solve each problem involving combinations. Seven workers decide to send a delegation of 2 to their supervisor to discuss their grievances. (a) How many different delegations are possible? (b) If it is decided that a certain employee must be in the delegation, how many different delegations are possible? (c) If there are 2 women and 5 men in the group, how many delegations would include at least 1 woman?

Use any or all of the methods described in this section to solve each problem. If a student has 8 courses to choose from, how many ways can she arrange her schedule if she must pick 4 of them?

Find each sum. $$\sum_{i=1}^{\infty} 3\left(\frac{1}{4}\right)^{i-1}$$

Use a formula to find the sum of each arithmetic series. The first 40 terms of the series \(a_{n}=5 n\)

Find the sum for each series. $$\sum_{i=1}^{100} 6$$

Find each sum. $$\sum_{i=1}^{\infty} 5\left(-\frac{1}{4}\right)^{i-1}$$