Find the specified $n th$ term in the expansion of the binomial. $(10 x-3 y)^{12}, n=10$

Use the letters A, B, C, D, E, and F. Write all possible selections of two letters that can be formed from the letters. (The order of the two letters is not important.)

Find the specified nth term in the expansion of the binomial. $(5 a+6 b)^{5}, n=5$

In given exercise, find the sum. Use a graphing utility to verify your result.

$$\sum_{n=0}^{15} 2\left(\frac{4}{3}\right)^n$$

In given exercise, find the sum of the finite arithmetic sequence.

-5+(-3)+(-1)+1+3+5

A shipment of 12 microwave ovens contains three defective units. A vending company has ordered four of these units, and because all are packaged identically, the selection will be random. What is the probability that (a) all four units are good, (b) exactly two units are good, and (c) at least two units are good?

Write the first five terms of the sequence defined recursively. Use the pattern to write the nth term of the sequence as a function of n. (Assume n begins with 1.) $a_{1}=25, a_{k+1}=a_{k}-5$

Evaluate $_nC_r$ using a graphing utility. $_{50}C_6$

Find the sum. Use a graphing utility to verify your result. $\sum_{n=1}^{4} 12\left(-\frac{1}{2}\right)^{n-1}$

Find the sum. Use a graphing utility to verify your result. $\sum_{n=0}^{15} 10\left(\frac{7}{6}\right)^{n}$

Find the binomial coefficient. ${ }_{8} C_{6}$

Write $1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6$ in factorial notation.

Determine whether or not the sequence is arithmetic. If it is, find the common difference. 4, 9, 14, 19, 24, . . .

The deck for a card game is made up of 108 cards. Twenty-five each are red, yellow, blue, and green, and eight are wild cards. Each player is randomly dealt a seven-card hand. What is the probability that a hand will contain (a) exactly two wild cards, and (b) two wild cards, two red cards, and three blue cards?