Permutations and Combinations

Let A and B be two sets containing 2 elements and
4 elements respectively. The number of subsets of
A \(\times\) B having 3 or more elements is :

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is:

Statement - 1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is emply is \({}^9{C_3}\).
Statement - 2: The number of ways of choosing any 3 places from 9 different places is \({}^9{C_3}\).

These are 10 points in a plane, out of these 6 are collinear, if N is the number of triangles formed by joining these points. then:

There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangement is :

In a shop there are five types of ice-cream available. A child buys six ice-cream.
Statement - 1: The number of different ways the child can buy the six ice-cream is \({}^{10}{C_5}\).
Statement - 2: The number of different ways the ch...

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

The set S = {1, 2, 3, ........., 12} is to be partitioned into three sets A, B, C of equal size. Thus \(A \cup B \cup C = S,\,A \cap B = B \cap C = A \cap C = \phi\). The number of ways to partition S is

At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can...

If the letter of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number

How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order

The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

If \({}^n{C_r}\) denotes the number of combination of n things taken r at a time, then the expression \(\,{}^n{C_{r + 1}} + {}^n{C_{r - 1}} + 2\, \times \,{}^n{C_r}\) equals

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is

The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by

Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4 and 5 without repetition. Total number of such numbers are :

Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are :

Number greater than 1000 but less than 4000 is formed using the digits 0, 1, 2, 3, 4 (repetition allowed). Their number is :

The sum of integers from 1 to 100 that are divisible by 2 or 5 is :