Chapter 6

A survey conducted among 300 adults show that 160 like to have their houses painted white and 140 like blue, Seventy-Four like both colors. How do not like either colors?

Two dice are rolled. Find the probability of obtaining each event. A sum of \(11,\) knowing that a six has occurred on one die.

A card is drawn at random from a standard deck of cards. Find the probability of obtaining: A king.

Find the coefficient of each. \(x^{3} y^{5}\) in the expansion of \((x+y)^{8}\)

A committee consists of nine members. Find the number of subcommittees that can be formed of each size. Two

Find the number of positive integers \(\leq 1976\) and divisible by: 2 or 3

Evaluate each. $$\frac{5 !}{4 !}$$

A survey conducted among 300 adult shows that 160 like to have their houses painted white and 140 like blue. Seventy-four like both colors. How many do not like either color?

Find the coefficient of each. $$x^{3} y^{5} \text { in the expansion of } (x+y)^{8}$$

A survey among 100 consumers shows that of the two laundry detergents, Lex and Rex, 45 like Lex, 60 like Rex, and 20 like both. How many surveyed do not like either of them?

Two dice are rolled. Find the probability of obtaining each event. A sum of \(11,\) knowing that one die shows an odd number.

A card is drawn at random from a standard deck of cards. Find the probability of obtaining: A club.

Find the coefficient of each. \(x^{4} y^{6}\) in the expansion of \((x-y)^{10}\)

Find the number of distinct words that can be formed by scrambling the letters in each word. TALLAHASSEE

A committee consists of nine members. Find the number of subcommittees that can be formed of each size. Five

Find the number of positive integers \(\leq 1976\) and divisible by: 3 or 5

Evaluate each. $$\frac{10 !}{3 ! 7 !}$$

Find the coefficient of each. $$x^{4} y^{6} \text { in the expansion of } (x-y)^{10}$$

Find the number of positive integers \(\leq 1000\) and \(n\) ot divisible by: 3 or 5

It is found that 65\(\%\) of the families in a town own a house, 25\(\%\) own a house and a minivan, and 40\(\%\) own a minivan. Find the probability that a family selected at random owns each of the following. A house, given that it owns a minivan.

A card is drawn at random from a standard deck of cards. Find the probability of obtaining: A king or a queen.

Find the coefficient of each. \(x^{2} y^{6}\) in the expansion of \((2 x+y)^{8}\)

A committee consists of nine members. Find the number of subcommittees that can be formed of each size. Six

Evaluate each. $$P(5,3)$$

Find the number of positive integers \(\leq 1976\) and divisible by: \(2,3,\) or 5

Find the coefficient of each. $$x^{2} y^{6} \text { in the expansion of } (2 x+y)^{8}$$

Find the number of positive integers \(\leq 1000\) and \(n\) ot divisible by: 5 or 6

It is found that 65\(\%\) of the families in a town own a house, 25\(\%\) own a house and a minivan, and 40\(\%\) own a minivan. Find the probability that a family selected at random owns each of the following. A minivan, given that it owns a house.

A card is drawn at random from a standard deck of cards. Find the probability of obtaining: A club or a diamond.

Find the coefficient of each. \(x^{4} y^{5}\) in the expansion of \((2 x-3 y)^{9}\)

A committee consists of nine members. Find the number of subcommittees that can be formed of each size. Seven

Find the number of positive integers \(\leq 1976\) and divisible by: \(3,5,\) or 7

Evaluate each. $$P(6,6)$$

Find the coefficient of each. $$x^{4} y^{5} \text { in the expansion of } (2 x-3 y)^{9}$$

Find the number of positive integers \(\leq 1000\) and \(n\) ot divisible by: \(2,3,\) or 5

The Sealords have three children. Assuming that the outcomes are equally likely and independent, find the probability that they have three boys, knowing that: The first child is a boy.

Two dice are rolled. Find the probability of obtaining: Two fives.

Using the binomial theorem, expand each. $$(x+y)^{4}$$

Find the number of ways a committee of three students and five professors can be formed from a group of seven students and 11 professors.

The Sealords have three children. Assuming that the outcomes are equally likely and independent, find the probability that they have three boys, knowing that: At least one child is a boy.

Two dice are rolled. Find the probability of obtaining: A five and a six.

Using the binomial theorem, expand each. $$(x-y)^{5}$$

Find the number of ways a committee of four students, four professors, and three administrators can be formed from a group of six students, eight professors, and five administrators.

Find the number of terms in the expansion of each expression. $$(a+b)(c+d+e)(x+y)$$

Find the number of positive integers \(\leq 1000\) and \(n\) ot divisible by: \(3,5,\) or 7

Using the alternate inclusion-exclusion formula, find the number of primes not exceeding: 75

The Sealords have three children. Assuming that the outcomes are equally likely and independent, find the probability that they have three boys, knowing that: The second child is a boy.

Two dice are rolled. Find the probability of obtaining: A sum of four.

Using the binomial theorem, expand each. $$(2 x-1)^{5}$$

Find the number of bytes that: Contain exactly eight \(0^{\prime} \mathrm{s}\)