Permutations and Combinations

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Across
  1. 4. 25 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
  2. 7. How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
  3. 9. How many diagonals can be draw in a pentagon?
  4. 11. A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?
  5. 12. In how many ways can the letters of the word 'LEADER' be arranged? (answer is a contraction)
  6. 13. A box contains 4 red, 3 white and 2 blue balls. Three balls are drawn at random. Find out the number of ways of selecting the balls of different colours
  7. 14. In how many way the letter of the word "APPLE" can be arranged?
  8. 15. There are 10 points in a plane out of which 4 are collinear Find the number of triangles formed by the points as vertices?
  9. 16. In how many ways six different rings can be worn on four fingers of one hand?
  10. 17. If you have 6 New Year greeting cards and you can to send them in 360 ways, to how many friends you can send this?
Down
  1. 1. Find the number of triangles which can be formed by joining the angular points of polygon of 8 sides as vertices.
  2. 2. How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes?
  3. 3. In a party every person shakes hand with every other person. If there are 105 handshakes, find the number of persons in the party.
  4. 5. Six parallel lines are intersected by 5 other parallel lines. The total number of parralellograms formed is? (answer is a contraction - shorter way to say it)
  5. 6. In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?
  6. 8. In how many waysways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
  7. 10. A two member committee comprising of one male and one female member is to be chosen from of five males and three females. Amongst the females. Ms. A refuses to be a member of the committee if Mr. B is taken as the member. In how many different ways can the committee be made?
  8. 16. In an examination paper, there are two groups each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any group. In how many ways can 5 questions be selected?