91Ó°ÊÓ

In Exercises 41 - 44, expand the binomial by using Pascals Triangle to determine the coefficients \( \left(x + 2y\right)^5 \)

In Exercises 45 - 56, find the indicated \( n \)th term of the geometric sequence. 7th term: \( 3, 36, 432, \cdots \)

Three people have been nominated for president of a class. From a poll, it is estimated that the first candidate has a \( 37\% \) chance of winning and the second candidate has a \( 44\% \) chance of winning. What is the probability that the third candidate will win?

In Exercises 53 - 60, find the coefficient of the term in the expansion of the binomial. Binomial \( \quad \quad \quad \) Term \( \left(x - 2y\right)^{10} \quad \quad \quad ax^8y^2 \)

In Exercises 53 - 60, the sample spaces are large and you should use the counting principles discussed in Section 9.6. 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. (a) What is the probability that a hand will contain exactly two wild cards? (b) What is the probability that a hand will contain two wild cards, two red cards, and three blue cards?

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

Two integers from 1 through 40 are chosen by a random number generator. What are the probabilities that (a) the numbers are both even, (b) one number is even and one is odd, (c) both numbers are less than 30, and (d) the same number is chosen twice?

From a group of \( 40 \) people, a jury of \( 12 \) people is to be selected. In how many different ways can the jury be selected?

A U.S. Senate Committee has \( 14 \) members. Assuming party affiliation was not a factor in selection, how many different committees were possible from the \( 100 \) U.S. senators?

American roulette is a game in which a wheel turns on a spindle and is divided into \( 38 \) pockets.Thirty-six of the pockets are numbered \( 1-36 \), of which half are red and half are black. Two of the pockets are green and are numbered \( 0 \) and \( 00 \) (see figure). The dealer spins the wheel and a small ball in opposite directions. As the ball slows to a stop, it has an equal probability of landing in any of the numbered pockets. (a) Find the probability of landing in the number \( 00 \) pocket. (b) Find the probability of landing in a red pocket. (c) Find the probability of landing in a green pocket or a black pocket. (d) Find the probability of landing in the number \( 14 \) pocket on two consecutive spins. (e) Find the probability of landing in a red pocket on three consecutive spins.