Answer:
a ) P₈ = 40320
b) P = 576
c) P = 1440
d) P = 24
Step-by-step explanation:
a ) 8 people sitting in a row without restrictions
simple Total ways = P₈ = 8!
P₈ = 8*7*6*5*4*3*2*1
P₈ = 40320
b) There are 4 men and 4 women and no two men or 2 women can sit next to each other
Let letters e women and numbers be men we have something like this
1 a 2 b 3 c 4 d
So we have the permutations of the four digits (men)
P₄ = 4!
P₄ = 4*3*2*1 = 24
And the permutations of the 4 women too equal to 24
Then total ways of sitting in a row in this case is
P = 24*24 = 576
c) There are 5 men and they have to sit next to each other
In this case we have 2 groups:
Group 1 5 men Group 2 3 women
We have two groups and the ways are
group men first group of women second 1 way
group of women first group of men second 2 way
Permutations within men group
P₅ = 5! = 5*4*3*2*1
P₅ = 120
Permutations within the women group
P₃ = 3! = 3*2*1
P₃ = 6
Total ways case c) T = 6*120*2 =
P(c) = 1440
d) There are four couples and each couple must be together
P₄ = 4! = 4*3*2*1
P₄ = 24
