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 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?

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?

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?

There are four balls of different colors. Two balls at a time are taken and arranged any way. How many such combinations are possible?

How many \(6\)-number combinations can be generated from the numbers from \(1\) to \(42\) inclusive, without repetition and with no regards to the order of the numbers?

Find the total number of combinations of three letters, J, R, T taken \(1\), \(2\), \(3\) at a time.

In how many ways can you invite one or more of your five friends in a party?

In Mathematics examination, a student may select \(7\) problems from a set of \(10\) problems. In how many ways can he make his choice?

How many committees can be formed by choosing \(4\) men from an organization of a membership of \(15\) men?

Roll a pair of dice. What is the probability that the sum of two numbers is \(11\)?

Roll two dice once. What is the probability that the sum is \(7\)?

In a throw of two dice, the probability of obtaining a total of \(10\) or \(12\) is