PERMUTATION AND COMBINATION - 8
nCr * r ! = nPr
nCr - selection of ‘r’ different objects out of n- different object
r! - arrangement of ‘r’ objects
nPr - arrangement of n - different objects taken ‘r’ at a time.
Q1. There are m points on a straight line AB & n points on the line AC none of them being the point A. Triangles are formed with these points as vertices, when
‘A’ is excluded. Ding the total number of ways.
2 points of line AB
& 1 point on line AC.
Vice versa
m c 2 X n c 1
+
n c 2 X m c 1
‘A’ is included. Find the total number of ways.
mc1 X nc1 + above answer.
Q2. 10 different chocolates & 20 different toffees.
In how many ways 3 chocolates and 4 toffees are given to a child ?
Sol :- permutation and combination
10 c 3 * 20 c 4
Explanation :-
20 c 4 means 20! / ( 20-4)! * 4!
Why we use X (multiply) because both the processes is done simultaneously
Permutation.
Quick Concept review.
Permutation :-
It is arrangement of object
Order of object is important.
Permutation of diff object can be calculated by npr
nPr = n! / (n-r)!
Combination :-
selection of object
Order of object is important.
Selection of diff objects can be calculated by nCr.
nCr = n! / (n-r)! * r!
Circular Permutation
Arrangement of objects on a circle is known as circular permutation. ( different objects )
A,B,C in a straight line 3! Arrangement
In a circle there are only 2 arrangement .
Clockwise & Anticlockwise arrangements are different.
( N - 1!)
Clockwise & Anticlockwise arrangement are same
( N - 1!) / 2
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