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Involve dialing the last four digits of a phone number that has an area code of 907 and an exchange of \(316 .\) The exchange consists of the first three digits of the seven-digit phone number. How many outcomes are there for dialing the last four digits of a phone number?

Use the Binomial Theorem to find the indicated term or coefficient. The third term in the expansion of \((x-4)^{6}\)

Find the rule for the geometric sequence having the given terms. $$\begin{array}{crr} n & 3 & 4 \\ \hline g(n) & -8 & -16 \end{array}$$

Use the Binomial Theorem to find the indicated term or coefficient. The fourth term in the expansion of \((x+3)^{6}\)

Involve dialing the last four digits of a phone number that has an area code of 907 and an exchange of \(316 .\) The exchange consists of the first three digits of the seven-digit phone number. How many possible outcomes are in the event that the first three (of the last four) digits you dial are 726 , in that order?

In how many different ways can five people be chosen to receive a prize package from a group of 50 people at the grand opening of a local supermarket?

Find the first four terms of the recursively defined sequence. $$b_{1}=\sqrt{3} ; b_{n}=\sqrt{\frac{b_{n-1}}{3}, n=2,3,4, \dots}$$

Find the sum. $$\sum_{i=0}^{5}(-3 i)$$

Find the sum. $$\sum_{i=0}^{10}(5+2 i)$$

Find the rule for the geometric sequence having the given terms. $$\begin{array}{ccc} n & 4 & 7 \\ \hline b_{n} & \frac{3}{16} & \frac{3}{128} \end{array}$$