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1. Permutations and Combinations

2. Basics : Permutation – arrangement
Combination – selection
• Out of n different things, if some or all the things are selected at a time,
then each of these selections is called a Combination
• Out of n different things, if r things are selected at a time, then the
number of selections is given by =
• and =
• + + + + …..
• The number of ways in which we can select is given by .

3. 1. In a party, each person has to give a handshake to the other person
only once. If the total number of handshakes exchanged in the party is
435, then find the number of persons in the party?
2. In how many ways can u invite at least one of your 8 friends to a party?
3. How many diagonals are there in an octagon?
4. How many rectangles are there in a chessboard?
5. Out of 5 boys and 4 girls, a team of 4 men can be selected. In how
many ways can u select the team, such that there is at least one girl in
the team?
Combination :

4. In a party, each person has to give a handshake to the other person only
once. If the total number of handshakes exchanged in the party is 435,
then find the number of persons in the party?
Ans :
Handshake ( selecting 2 hands at a time) = = 435
( )
= 435

 n = 30
 Number of persons = 30
1.
number of persons in the party = 30

5. In how many ways can u invite atleast one of your 8 friends to a party?2.
 + + …..
 We know that + + + + …..
 X=1 , n =8


6. How many diagonals are there in an octagon?3.
Ans :
To draw a polygon with n sides, we require n non-collinear points. The
total number of line segments that can be drawn using n non-collinear
points is given by
Number of diagonals = - n ( n = number of sides )
In the given question,
N = 8
=> Number of diagonals = - 8
Number of diagonals = 20

7. How many rectangles are there in a chessboard?4.
Ans :
If a set of m parallel lines intersect with another set of n parallel lines then
the total number of parallelograms formed are
Total number of parallelograms formed in chess board =
= 1296
Total number of squares in a chessboard = 204
 Total number of rectangles = 1296 – 204 = 1092.
Total number of rectangles = 1092

8. Out of 5 boys and 4 girls, a team of 4 should be selected. In how many
ways can u select the team, such that there is atleast one girl in the
team?
5.
Ans :
1G, 3B ; 2G, 2B ; 3G, 1B ; 4G or ( any 4 – 4B )
Number of ways = + + + = 121
OR
Number of ways =
= 121
Number of ways = 121

9. Subscribe to :
Problems for practice are given in the description of the video.