A deck of 52 cards is taken. From this, 4 cards are to be chosen such that exactly two of them are hearts and exactly two of them are kings. In how many ways can this be done?

The number of ways in which 6 different marbles can be put in two boxes of different sizes so that no box remains empty is

There are 10 people seated in two rows (5 in 1 row) and there are two types of food items. Each row can be served any of the two food items but it must be different from the other row. In how many ways the food can be served?

How many numbers of four digit can be formed with the digits 0, 1, 2, 3 (repetition of digits is not allowed)?

From a group of 7 laptops, 6 mobile phones and 8 watches, 4 gadgets are to be chosen such that there is at least one gadget of each type. In how many ways can it be done?

Given below are two quantities named A & B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose the possible answer. Quantity A∶ Suppose there are 4 teachers, 6 students and 3 guardians. What are the various ways in which a committee of 7 members can be formed, such that the committee has at least 3 students and 2 guardians? Quantity B∶ 590.

Out of 5 men and 3 women, a committee of 3 persons is to be formed. In how many ways can it be formed selecting at least 2 women?

In how many ways we can arrange the letters of the word “ARRAGEET”?

A palindrome is a word which is similar if read from backwards. Eg ‘ARORA’. Find the number of such 5 letter palindromes.

There are 10 seats around a circular table. If 8 men and 2 women have to be seated around a circular table, such that no two women have to be separated by at least one man. If P and Q denote the respective number of ways of seating these people around a table when seats are numbered and unnumbered, then P : Q equals :

In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every other student. It was found that in 45 games both the players were girls, and in 190 games both were boys. The number of games in which one player was a boy and the other was a girl is

In a party, every person shakes hands with every other person. If there occur a total of 120 handshakes in the party, how many people were present at the party?

In a four digit number, first digit is greatest and last digit is smallest. Sum of middle two digits is even. How many such four digit numbers, having all digits different, can be there if first digit is 9?

There are 3 bowls and 5 nuts. All these nuts are to be distributed into three bowls where any bowl can contain any number of nuts. In how many ways these nuts can be distributed into these bowls if all the bowls and all the nuts are different?

How many codes are there starting with 6 or ending with 8?

Six different pencils and three bags are taken. Each pencil is to be put in one of these bags. No bag should remain empty and all bags should not have same number of pencils. In how many ways can this be done?

Three pen companies A, B and C launched 6, 5 and 6 different models respectively. Find the ways in which they can be displayed in a case with 17 slots such that the models of no two companies are mixed together.

In how many ways the letters of word FACETIOUS can be arranged so that the first three letters are in dictionary order?

The number of ways in which 20 different flowers of two colors can be set alternately on a necklace, there being 10 flowers of each colour, is

In a simultaneous throw of two dice, what is the probability of getting a total of 7?

If a license plate has to be made where the first 4 places are numbers from 0 to 9 and the last two letters are made from the alphabets A to F, how many different license plates are possible where the repetition of any letter or number is not allowed?

How many different words can be formed with the letters of the word ‘M A I M I T A L’ such that each of the word begins with L and ends with T?

How many codes (without confusion) will be there that are not starting with 1 and not ending with 1?

How many codes are there for which no such confusion can arise?

A man has to travel from Allahabad to Lucknow and then from Lucknow to Kolkata. If there are 5 routes from Allahabad to Lucknow and 4 routes to go from Lucknow to Kolkata, then how many options are available for the man to travel from Allahabad to Kolkata via Lucknow?

In how many ways can 5 boys and 7 girls be arranged in a row so that no two boys are together?

Find the number of possible triangles using points on the sides of any triangle ABC having “a” points on side BC, “b” points on side AC, “c” points on side AB excluding the points at vertices.