Statistics

In a class of \(40\) students, \(27\) like Calculus and \(25\) like Chemistry. How many like both Calculus and Chemistry?

A club of \(40\) executives, \(33\) like to smoke Marlboro and \(20\) like to smoke Philip Morris. How many like both?

A survey of \(100\) persons revealed that \(72\) of them had eaten at restaurant P and that \(52\) of them had eaten at restaurant Q. Which of the following could not be the number of persons in the surveyed group who had eaten at both P and Q?

The probability for the ECE board examinees from a certain school to pass the subject Mathematics is \(3/7\) and for the subject Communications is \(5/7\). If none of the examinees fails both subject and there are \(4\) examinees who pass both subjects, find the number of examinees from that school who took the examinations.

In a commercial survey involving \(1000\) persons on brand preference, \(120\) were found to prefer brand x only, \(200\) prefer brand y only, \(150\) prefer brand z only, \(370\) prefer either brand x or y but not z, \(450\) prefer brand y or z but not x and \(370\) prefer either brand z or x but not y. How many persons have no brand preference, satisfied with any of the three brands?

A toothpaste firm claims that in a survey of \(54\) people, they were using either Colgate, Hapee or Close-up brand. The following statistics were found: \(6\) people used all three brands, \(5\) used only Hapee and Close-up, \(18\) used Hapee or Close-up, \(2\) used Hapee, \(2\) used only Hapee and Colgate, \(1\) used Close-up and Colgate, and \(20\) used only Colgate. Is the survey worth paying for?

How many four-letter words beginning and ending with a vowel without any letter repeated can be formed from the word "personnel"?

Five different mathematics books, \(4\) different electronics books and \(2\) different communications books are to be placed in a shelf with the books of the same subject together. Find the number of ways in which the books can be placed.

The number of ways can \(3\) nurses and \(4\) engineers be seated on a bench with the nurses seated together is

If \(15\) people won prizes in the state lottery (assuming that there are no ties), how many ways can these \(15\) people win first, second, third, fourth and fifth prizes?

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 are there if the letters PNRCSE are taken six at a time?

In how many ways can \(6\) distinct books be arranged in a bookshelf?

What is the number of permutations of the letters in the word BANANA?

A PSME unit has \(10\) ME's, \(8\) PME's and \(6\) CPM's. If a committee of \(3\) members, one from each group is to be formed, how many such committees can be formed?

In how many ways can a PSME 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?

Four different colored flags can be hung in a row to make coded signal. How many signals can be made if a signal consists of the display of one or more flags?

In how many ways can \(4\) boys and \(4\) girls be seated alternately in a row of \(8\) seats?

There are four balls of four different colors. Two balls are taken at a time and arranged in a definite order. For example, if a white and a red balls are taken, one definite arrangement is white first, red second, and another arrangement is red first, white second. How many such arrangements are possible?

How many different ways can \(5\) boys and \(5\) girls form a circle with boys and girls alternate?