Permutations and Combination Maths - Permutations and Combination

A question paper has two parts, A and B, each containing 10 questions. If a student has to choose 8 from part A and 5 from part B, in how many ways can he choose the questions?

In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate.

In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together?

In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all persons of the same nationality sit together?

Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms formed.

A question paper has 6 questions. How many ways does a student have to answer if he wants to solve at least one question?

A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.

A student passes an examination if he secures a minimum in each of the 7 subjects. Find the number of ways a student can fail.

There are 4 doctors and 8 lawyers in a panel. Find the number of ways for selecting a team of 6 if at least one doctor must be in the team.

How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?

How many quadratic equations can be formed using numbers from 0, 2, 4, 5 as coefficients if a coefficient can be repeated in an equation?

A student finds 7 books of his interest but can borrow only three books. He wants to borrow the Chemistry part II book only if Chemistry Part I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.

Ten students are to be selected for a project from a class of 30 students. There are 4 students who want to be together either in the project or not in the project. Find the number of possible selections.

Nine friends decide to go for a picnic in two groups. One group decides to go by car and the other group decides to go by train. Find the number of different ways of doing so if there must be at least 3 friends in each group.

Find the number of words that can be formed by using all the letters in the word REMAIN. If these words are written in dictionary order, what will be the 40th word?

A question paper has two sections. Section I has 5 questions and section II has 6 questions. A student must answer at least two questions from each section among 6 questions he answers. How many different choices does the student have in choosing questions?

In how many ways can a boy invite his 5 friends to a party so that at least three join the party?

There are 12 distinct points A, B, C, …, L, in order, on a circle. Lines are drawn passing through each pair of points.
(i)How many lines are there in total?
(ii)How many lines pass through D?
(iii)How many triangles are determined by lines?
(iv)How many triangles have on vertex C?

A group consists of 9 men and 6 women. A team of 6 is to be selected. How many of possible selections will have at least 3 women?

A committee of 10 persons is to be formed from a group of 10 women and 8 men. How many possible committees will have at least 5 women? How many possible committees will have men in majority?

Find the number of permutations of letters in each of the following words.
(i) DIVYA
(II)SHANTARAM
(III)REPRESENT
(IV)COMBINE
(V)BAL BHARATI

Find the number of ways so that letters of the word HISTORY can be arranged as

(A) Y and T are together

(B)Y is next to T

(C)there is no restriction

(D)begin and end with a vowel

(E)end in ST

(F)begin with S and end with T