## Questions on Counting Techniques and Probability

1. How many 4 even numbers can be formed by using 7,4,6,9 ?

2. How many 4 digit numbers can be formed by using 5,7,9,0?

3. How many 4 digit numbers can be formed by using 5,7,9,0 when the digits can be repeated ?

4. How many words with or without meaning can be formed using letters of word “PENCIL”?

5. A suitcase has number lock with 3 wheels with digits 0 to 9. How many unsuccessful attempts can be made to open it?

6. How many words with or without meaning can be found using

- PENCIL but it begins with P.
- Starting with P and ends with E.
- Begins with P but doesn’t end with E.
- E and N are always together.
- E and N are never together.
- N is always next to E.
- It starts with “PEN”.

7. In how many ways can 5 boys and 5 girls be seated in a row such that

- No two girls sit together.
- All the girls are never together.
- All girls together and all boys together.

8. How many arrangement of word “DAUGHTER” are possible such that

- Vowels are always together.
- Vowels are never together.
- Vowels occupy odd places.

9. In how many ways can 3 brothers and 3 sisters can stand in a row for a group photograph if brothers and sisters alternates?

10. How many arrangements of the HARYANA are possible?

11. How many ways can a team of 11 players be selected of 16 players.

12. In how many ways can a committee be formed of 5 members from 6 men and 5 women such that

- It includes 2 women.
- It includes at least 2 women.

13. In how many ways 2 students can be chosen from the class of 20 students?

14. Three gentlemen and three ladies are candidates for two vacancies. A voter has to vote for two candidates. In how many ways can one cast his vote.

15. 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?

16. In a party every person shakes hands with every other person. If there are 105 hands shake, find the number of person in the party.

17. A box contains 10 balls out of which 3 are red and rest are blue. In how many ways can a random sample of 6 balls be drawn from the bags, so that at the most 2 red balls are included in the sample and no sample has all the 6 balls of the same colour.

18. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is multiple of 3 or 5?

19. A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

20. In a box there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

21. There are three unbiased coins are tossed. what is the probability of getting at most two heads?

22. Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

23. In a class there are 15 boys and 10 girls. 3 students are selected at random, what is the probability that one girl and two boys are selected?

24. In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

25. From a pack of 52 cards, two cards are drawn at random. What is the probability of both cards being kings?

26. Two dice are tossed. What is the probability that total is a prime number?

27. A card is drawn from a pack of 52 cards. What is the probability of getting a queen of club or a king of heart?

28. A bag contains 4 white, 5 red, and 6 black balls. Three balls are drawn at random. What is the probability that all are red?

29. Two cards are drawn together from a pack of 52 cards. What is the probability that one is a spade and one is heart?

30. One card is drawn at random from a pack of 52 cards. What is the probability that the card is drawn is a face card (J,Q,K only)?

31. A bag contains 6 black and 8 white balls. One ball is drawn. What is the probability that the ball drawn is white?