How many 4 digit numbers can be formed without repeating any digit, from the following digits 1, 2, 3, 4 and 6.

How many permutations can be made out of the letters of the word ENGINEERING?

How many ways can 3 men and 4 women be seated on a bench if the women are to be together?

In how many ways can 5 people line up to pay their electric bills?

In how many ways can 5 people line up to pay their electric bills if two particular persons refuse to follow each other?

How many ways can 7 people be seated at a round table?

In how many relative orders can we seat 7 people at a round table with a certain 3 people side by side.

In how many ways can we seat 7 people in a round table with a certain 3 people not in consecutive order?

The captain of a baseball team assigns himself to the 4th place in the batting order. In how many ways can he assign the remaining places to his eight teammates if just three men are eligible for the first position?

In how many ways can PICE chapter with 15 directors choose a president, a vice-president, a secretary, a treasurer, and an auditor, if no member can hold more than one position?

How many ways can a committee of five may be selected from an organization with 35 members?

How many line segments can be formed by 13 distinct point?

In how many ways can a hostess select six luncheon guests from 10 women if she is to avoid having a particular two of them together at the luncheon?

A semiconductor company will hire 7 men and 4 women. In how many ways can the company choose from 9 men and 6 women who qualified for the position?

How many ways can you invite one or more of five friends to a party?

A bag contains 4 red balls, 3 green balls, and 5 blue balls. The probability of not getting a red ball in the first draw is:

Which of the following cannot be a probability?

A bag contains 3 white and 5 black balls. If two balls are drawn in succession without replacement, what is the probability that both balls are black?

8-20. A bag contains 3 white and 5 red balls. If two balls are drawn at random, find the probability that both are white.

In Problem 8-20, find the probability that one ball is white and the other is red.

In Problem 8-20, find the probability that all are of the same color.

The probability that both stages of a two-stage rocket function correctly is 0.92. The reliability of the first stage is 0.97. The reliability of the second stage is:

Ricky and George each throw two dice. If Ricky gets a sum of 4, what is the probability that George will get less.

Two fair dice are thrown. What is the probability that the sum shown on the dice is divisible by 5?

An urn contains 4 black balls and 6 white balls. What is the probability of getting one black ball and one white ball in two consecutive draws from the urn?

If three balls are drawn in succession from 5 white and 6 black balls, the second is not replaced before the third draw. Find the probability that all are of one color, if the first ball is replaced immediately while drawing black balls from the bag.

8-28. A first bag contains 5 white balls and 10 black balls and a second bag contains 20 white and 10 black balls. The experiment consists of selecting a bag and then drawing a ball from the selected bag. Find the probability of drawing a white ball.

In Problem 8-28, find the probability of drawing a white ball from the first bag.

If seven coins are tossed simultaneously, find the probability that they will just have three heads.

If seven coins are tossed simultaneously, find the probability that there will be at least six tails.

A face of a win is either head or tail. If three coins are tuned, what is the probability of getting three tails?

The face of a coin is either head or tail. If three coins are tossed, what is the probability of getting three tails or three heads?

Five fair coins were tossed simultaneously. What is the probability of getting three heads and two tails?

Throw a fair coin five times. What is the probability of getting three heads and two tails?

The probability of getting a credit in an examination is 1/3. If three students are selected at random, what is the probability that at least one of them got a credit?

There are three short questions in a mathematics test. For each question, one (1) mark will be awarded for a correct answer and no mark for a wrong answer. If the probability that Mary correctly answers a question in a test is 2/3, determine the probability that Mary gets two marks.

A marksman hits 75% of all his targets. What is the probability that he will hit exactly 4 of his next 10 shots?

A two-digit number is chosen randomly. What is the probability that it is divisible by 7?

One box contains four cards numbered 1, 3, 5, and 6. Another box contains three cards numbered 2, 4, and 7. One card is drawn from each bag. Find the probability that the sum is even.

Two people are chosen randomly from 4 married couples. What is the probability that they are husband and wife?

One letter is taken from LEVEL at random, and each of the words PARALLEL. What is the probability of getting the same letter?

In a shooting game, the probabilities that Botoy and Toto will hit a target is 2/3 and 3/4 respectively. What is the probability that the target is hit when both shoot at it once?

A standard deck of 52 playing cards is well shuffled. The probability that the first four cards dealt from the deck will be the four aces is closest to:

A card is chosen from a pack of playing cards. What is the probability that it is either red or a picture card?

In a poker game consisting of 5 cards, what is the probability of holding 2 2 aces and 2 Queens?

Dennis Rodman sinks 50% of all his attempts. What is the probability that he will make exactly 3 of his next 10 attempts?

There are 10 defectives per 1000 items of a product in a long run. What is the probability that there is one and only one defective in a random lot of 100.

The UN forces for Bosnia uses a type of missile that hits the target with a probability of 0.3. How many missiles should be fired so that there is at least an 80% probability of hitting the target?

In a dice game, one fair die is used. The player wins P20.00 if he rolls either 1 or 6. He losses P10.00 if he turns up any other face. What is the expected winning for one roll of the die?

In the complex number 3 + 4i, the absolute value is:

In the complex number 8 – 2i, the amplitude is:

(6 cis 120°)(4 cis 30°) is equal to:

(30 cis 80°) / (10 cis 50°) is equal to:

The value of x + y in the complex equation 3 + xi = y + 2i is:

Multiply (3 – 2i) (4 + 3i).

Divide (4 + 3i) / (2 – i).

Find the value of $$i^9$$ .

Simplify $$i^{1997} + i^{1999}$$ , where i is an imaginary number.

Expand (2 + ³√(–9)).

Write -4 + 3i in polar form.

Simplify: $$i^{30} - 2i^{25} + 3i^{17}$$ .

Evaluate the value of √-10 × √-7.

Perform the indicated operation: √-9 × ³√-343.

What is the quotient when $$4 + 8i$$ is divided by $$i^3$$ ?

What is the exponential form of the complex number 4 + 3i?

What is the algebraic form of the complex number $$13 e^{i 67.38°}$$ ?

Solve for x that satisfy the equation x² + 36 = 9 – 2x².

Evaluate ln(5 + 12i).

Add the given vectors: (–4, 7) + (5, –9).

Find the length of the vector (2, 1, 4).

In a proportion of four quantities, the first and the fourth terms are referred to as the:

Convergent series is a sequence of decreasing numbers or when the succeeding term is _____ than the preceding term.

It is the characteristic of a population which is measurable.

The quartile deviation is a measure of:

In complex algebra, we use a diagram to represent a complex plane commonly called:

A Series of numbers which are perfect square numbers (i.e. 1,4,9,16, …) is called:

A sequence of numbers where every term is obtained by adding all the preceding terms such as 1,5,14,30, … is called:

The graphical representation of the cumulative frequency distribution in a set of statistical data is called:

A sequence of numbers where the succeeding term is greater than the preceding term is called:

The number 0.123123123 … is

An array of m x n quantities which represent a single number system composed of elements in rows and column is known as:

The characteristic is equal to the exponent of, when the number is written in:

Terms that differ only in numeric coefficients are known as:

The logarithm of a number to the base e (2.718281828…) is called:

The ratio or product of two expressions in direct or inverse relation with each other is called:

In any square matrix, when the elements any two rows are exactly the same determinants is:

Two or more equations are equal if and only if they have the same:

What is a possible outcome of an experiment called:

If the roots of an equation are zero, then they are classified as:

A complex number associated with a phase-shifted sine wave in polar form whose magnitude is in RMS and angle is equal to the angle of the phase-shifted sine wave is known as:

In raw data, the term which occurs most frequently is known as:

Infinity minus infinity is:

Any number divided by infinity is equal to:

The term in between any two terms of an arithmetic progression is called:

Any equation which, because of some mathematical process, has acquired an extra root is sometimes called a:

A statement that one mathematical expression is greater than or less than another is called:

A relation in which every ordered pair (x, y) has one and only one value of y that corresponds to the values of x, is called:

Find the length of the vector (2, 4, 4).

What is the magnitude of the vector F = 2i + 5j + 6k?