PERMUTATION AND COMBINATION - 5
Permutation = arrangement of object
Combination = selection of object
Different Object & Alike Object
Different object -
Eg :- a,b,c,d.
Alike Object -
Eg :- a,a,a,a.
Permutation = arrangement of object
Types :-
Permutation / Arrangement of Different object
Eg :- Permutation / arrangement of ‘n’ different objects is given a factorial of ‘n’.
Permutation / Arrangement of Alike object
Eg :- permutation of ‘n’ different objects is given a factorial of ‘n’.
Combination = selection of object
Types :-
Combination / Selection of Different object
Eg :- permutation of ‘n’ different objects is given a factorial of ‘n’.
Combination / Selection of Alike object
Eg :- permutation of ‘n’ different objects is given a factorial of ‘n’.
NUMERICAL
Q :- 4 BOYS & 4 GIRLS are to be arranged in a straight line. In how many ways this can be done.
Answer the following and fulfil the condition.
Without any restriction
It means 8 objects = 8!
If all boys are together
Box method : -
Boys can be arranged 4! ( internal arrangement inside box )
Girl + boy box = 5!
Answer = 4! * 5!
If all boys are together & all girls are also together.
Box method : -
Boys can be arranged 4! ( internal arrangement inside box )
Girls can be arranged 4! ( internal arrangement inside box )
Girl box + boy box = 2!
Answer = 4! * 2! * 2!
If boys are separated ( no two boys are together )
GAP method : -
Girls can be arranged 4!
BOYS are arranged in Gap = ( total Gap = 5 )
Answer = 4! * 5*4*3*2
If no two boys are together , no two girls are together.
GAP method : -
Girls can be arranged 4!
BOYS are arranged in 4!
Gap must be maintain = 2
Answer = 4! * 2 * 4!
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