Permutations and combinations

Permutations and Combinations : Permutations and Combinations Session-1 7/23/2010 Pathfinder Education Services

Agenda : Agenda What is Fundamental Principle of counting (FPC) Various applications of FPC What you should not expect from today’s session Unreasonably tough questions Short cuts or tricks Everything that concerns Permutations and combinations. What you should surely expect from today’s session Conceptual clarity of FPC. 7/23/2010 Pathfinder Education Services

What is FPC ? : What is FPC ? 7/23/2010 Pathfinder Education Services One task m1 2nd task m2 Both Tasks can be done in m1 x m2

In how many ways can a man travel from Bhopal to Delhi via Agra if there are 4 ways to travel from Bhopal to Agra and 5 ways to travel from Agra to Delhi. : In how many ways can a man travel from Bhopal to Delhi via Agra if there are 4 ways to travel from Bhopal to Agra and 5 ways to travel from Agra to Delhi. 7/23/2010 Pathfinder Education Services

Slide 5 : 7/23/2010 Pathfinder Education Services In how many ways can a man travel from Bhopal to Delhi via Agra or Jaipur if there are 4 ways to travel from Bhopal to Agra and 5 ways to travel from Agra to Delhi. And there are 3 ways to travel from Bhopal to Jaipur and 2 ways to travel from Jaipur to Delhi 7/23/2010 Pathfinder Education Services

For the IIFA awards there are some nominees for the lifetime achievement awards. Of the nominees, 3 are previous superstars, 4 are previous male stars and 5 are past female stars. If all of them have an equal chance of being awarded, in how many ways can the award be given? : For the IIFA awards there are some nominees for the lifetime achievement awards. Of the nominees, 3 are previous superstars, 4 are previous male stars and 5 are past female stars. If all of them have an equal chance of being awarded, in how many ways can the award be given? 7/23/2010 Pathfinder Education Services

Slide 7 : 7/23/2010 Pathfinder Education Services A secretary and Dy. Secretary are to be chosen from a class of 20 boys and 15 girls. It has been decided by the college administration that the secretary must be a boy and the Dy secretary must be a girl. In how many ways can a team of Secretary and Dy. Secretary be chosen. In how many ways can the team be chosen if two boys Nilanjan and Niket do not want to work with any of two girls Haritha and Aarti.

Slide 8 : 7/23/2010 Pathfinder Education Services 7/23/2010 Pathfinder Education Services In a survey there are 5 true and false type questions. Only a few people answered the survey. No two people had the same sequence of answers. What is the maximum possible number of people who answered the survey?

Slide 9 : 7/23/2010 Pathfinder Education Services In how many ways can 4 people sit on 4 available seats ? Introduction of P(n,r)

Slide 10 : 7/23/2010 Pathfinder Education Services In how many ways 3 seats can be occupied by 4 people or in how many ways 3 people can sit on 4 seats ?

Slide 11 : 7/23/2010 Pathfinder Education Services How many numbers are there between 100 and 1000 so that every digit is either 2,3 or 4.

Slide 12 : 7/23/2010 Pathfinder Education Services How many 3 digit numbers can be formed by the digits 1 to 7 if repetition of digits is allowed Repetition of digits is not allowed

Slide 13 : 7/23/2010 Pathfinder Education Services How many three digit even numbers can be formed using the digits 0,2,3,4,5,7. Rep allowed

Slide 14 : 7/23/2010 Pathfinder Education Services How many three digit numbers are even and positive. Repetition of the digits is allowed.

Slide 15 : 7/23/2010 Pathfinder Education Services Arrangements when some things are repeated. How many words can be formed from the letters of the word TWITTER.

Slide 16 : 7/23/2010 Pathfinder Education Services How many 5 digit numbers can be formed from the digits 1,22,3,4

Slide 17 : 7/23/2010 Pathfinder Education Services How many words can be formed from the letters of the word DIMPLE ? How many of them start with D and end with E? In how many of them the relative position of I and E remains unchanged

Slide 18 : 7/23/2010 Pathfinder Education Services How many ways to arrange n different items if r of them must be together. 4Boys and 3 girls are to be seated in a linear fashion such that all the three girls must sit together.

Slide 19 : 7/23/2010 Pathfinder Education Services How many words can be formed from the letters of the word DIMPLE ? How many of them start with D and end with E? In how many of them the relative position of I and E remains unchanged

Slide 20 : 7/23/2010 Pathfinder Education Services In how many ways can 6 B and 5 girls sit together so that, All the girls sit together No two girls sit together Girls and boys alternate. For the above question what happens if there are 6 Boys and 6 girls

Slide 21 : 7/23/2010 Pathfinder Education Services Thank you