SOLUTION: 1) How many ways can 3 boys and 3 girls stand in a line if
a) There are no restrictions.
b) All boys must stand next to each other.
c) all boys and all girls stand alternately b
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Permutations
-> SOLUTION: 1) How many ways can 3 boys and 3 girls stand in a line if
a) There are no restrictions.
b) All boys must stand next to each other.
c) all boys and all girls stand alternately b
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Question 1207205: 1) How many ways can 3 boys and 3 girls stand in a line if
a) There are no restrictions.
b) All boys must stand next to each other.
c) all boys and all girls stand alternately by gender.
d) Two particular boys must stand next to each other and at the same time two particular girls must stand next to each other
e) Two particular boys must stand next to each other and at the same time two particular girls must not stand next to each other
2) How many ways can 4 boys and 4 girls stand in a circle if
a) There are no restrictions.
b) All boys must stand next to each other.
c) all boys and all girls stand alternately by gender.
d) Two particular boys must stand next to each other and at the same time two particular girls must stand next to each other
e) Two particular boys must stand next to each other and at the same time two particular girls must not stand next to each other
(a) In (3+3)! = 6! = 720 different ways.
(b) 4*3!*3! = 4*6*6 = 4*36 = 144 different ways.
The factor 3! is for all possible permutations of 3 girls inside the set of girls.
The factor 3! is for all possible permutations of 3 boys inside the set of boys.
The factor 4 is for different possible placements of the group of boys in the line of girls.
(c) 2*3!*3! = 2*6*6 = 2*36 = 72.
Factor 3! is for all possible permutations in the set of 3 girls.
Factor 3! is for all possible permutations in the set of 3 boys.
Factor 2 is to account who is standing first in a line: a boy or a girl.
Do not post so many questions in one post.
Separate the set of your questions in different posts.
