A coin and a six-faced die are tossed simultaneously. How many different possible outcomes are there?

Kannan knows only Tamil, Malayalam and Marathi. Roy knows only Bengali and Punjabi. Vijay knows all these languages. In how many different ways can Vijay get a message from Kannan and pass it on to Roy?

Five roads lead to the top of a mountain. In how many ways can a tourist go up and down the mountain? What is the answer if the tourist must not retrace his steps?

In a class there are 53 girls and 47 boys. In how many ways, can two representatives, one of each sex, be selected?

Consider the suburban stations Beach, Fort, Park, Nungambakkam and Kodambakkam in Chennai. If there are 1500 passengers boarding at Beach, assuming that everyone of these passengers would get down at or before Kodambakkam, in how many possible ways can they get down?

Find the number of seven-letter words that can be formed by using the letters A, B, C, X, Y and Z.

At a dinner party, an individual must choose a roti item, a rice item, a subji item and a dessert item. The roti item must be one of butter naan, rumaali roti, or chapaathi. The rice item must be one of lemon rice, vegetable pulav and Chinese fried rice. The subji item must be one of vendaikaay poriyal (fried bhendi), alu mutter, malai kofta, baingan bartha (brinjal curry) or paneer palak. The dessert item must be chosen from ice-cream and fruit salad. How many possible dinners are there?

A group of six people includes Selvi and Lakshman. Find the number of ways of seating them provided there should be at least one person between Selvi and Lakshman.

In a buffet you must choose a total of seven dishes out of 10 South Indian dishes and eight North Indian dishes by choosing not less than two dishes from the two set of dishes. Find the number of ways of doing this.

A rich woman owns three engineering colleges and four medical colleges. She has six daughters and a son. Before she dies, she wants to give one college to each of her offspring. If the son wants to get only a medical college, in how many ways can the rich women distribute her colleges to her children?

From an assembly consisting of 132 MLAs, in how many ways can ministers be alloted for 15 portfolios?

How many five-letter words can be formed by using the letters of the word RIDAGNES without repetition?

How many six-digit numbers can be formed by using the digits 1, 2, 3, 4, 5, 6, 7, 8 without repetition?

A class consists of 42 students. In how many ways can a sports committee having the posts of President, Secretary, Joint Secretary and Treasurer be formed? If there is one class representative and if she or he has to be the president of the sports committee, in how many ways can this be achieved? If the class representative need not be the president but only has to be one of the committee members, in how many ways can such committees be formed?

Five children and four adults go for camping. There are eight sleeping bags inside the tent, and one sleeping bag is kept outside the tent. In how many ways can the campers occupy the sleeping bags if only an adult is allowed to use the sleeping bag outside?

How many even nine-digit numbers can be formed using the digits from 1 to 9 without repetition of the digits?

How many one-to-one functions can be formed using a set containing three elements into a set containing seven elements?

A committee consisting of five people has to be formed out of a class consisting of 25 students. In how many ways can this be achieved?

A class consists of 16 girls and 14 boys.

How many numbers between 1 and 10⁴ contain exactly one 8 and one 9?

Fifteen girls and six boys have to be seated in a row in such a way that no two boys sit next to each other.

How many seating arrangements are possible?

How many six-digit integers are divisible by 4?

Hint: For a number to be divisible by 4 the last two digits must be one of the following pairs: (00,04,08,…,96).

In how many ways can the letters in SANGAILAKKIYAM be arranged? In these arrangements how many have all the A's together?

Andaal and Meera are friends and they keep talking to each other. A group of 10 students including these two meet. The group decides that there must be five persons between Andaal and Meera. How many seating arrangements are possible?

From a choice of 12 colours, a flag consisting of three bands of different colours has to be created? How many such flags can be formed?

In all there are 735 teachers employed by five engineering colleges, including the principals. The managements of the five colleges would like to form an academic council consisting of 50 teachers from this group. How many such councils can be formed? If the council must necessarily include all the principals, how many councils can be constituted?

Twenty-eight persons are to be partitioned into five teams such that the first team has seven members, the second and the third team each has three members, the fourth team has 10 members and the fifth team has three members. How many partitions are possible?

How many automobile licence plates are possible if the inscription of each contains two different letters followed by three different digits?

The licence plates for vehicles registered in Delhi consists of three letters of the English alphabet followed by 1, 2, 3 or 4 digits. The letter on the extreme left has to be D. Zero is not allowed immediately after the letters. Find the number of all possible licence plates.

Rani has a 10-day holiday. She has 15 friends. She would like to meet exactly one of her friends during each of these 10 days. In how many ways can she arrange the meetings? If she does not want to meet the same friend twice, how many arrangements are possible?

A committee of 12 is to be selected from 10 men and 10 women. In how many ways can the selection be carried out if

In computers, each character is represented by a sequence of eight zeros and ones called a bit pattern. How many bit patterns are there? How many of them will have five ones and how many of them will have an even number of zeros?

A gym coach must select 11 seniors to play on a football team. If he can make his selection in 12,376 ways, how many seniors are eligible to play?

In how many ways can we place 10 identical green cubes, six identical red cubes and four identical yellow cubes in eight boxes?