Answer:
a ) P(8) = 40320
b ) Pt(7) = 10080
c ) P(t) = 48
d ) P(4) = 24
e ) P(4) = 24
Step-by-step explanation:
a) Without restrictions 8 persons can seat according to
P(8) = 8 ! P(8) = 8*7*6*5*4*3*2*1
P(8) = 40320
b) Two people must sit next to each other
Let A and B are a unit in the group
Then we have 7 elements
P₁(7) = 7 ! P₁(7) = 7*6*5*4*3*2*1
P₁(7) = 5040
Now this number is for arrangement A B we should add the same number now with B A
Then P₂(7) = 5040 and
Pt(7) = 10080
c) There are 4 men and 4 women that can not sit next to each other
Let A B C and D stands for men and 1 2 3 and 4 women
A 1 B 2 C 3 D 4
This kind of arrangement is what we are loking for
If we change men and women are still we have
P₁(4) = 4! P₁(4) = 4*3*2*1
P₁(4) = 24
Now we dont move men but women
P₂(4) = 24
In this case P(t) = 24+24
P(t) = 48
d) If five men is a group we have only 4 elements
P(4) = 4! P(4) = 4*3*2*1
P(4) = 24
e) If we have four couples we only have four elements
P(4) = 24
