a) a insists on sitting with b.
That's the number of arrangements of
the four things {ab, c, d, e}, which is 4! or 24.
PLUS
the number of arrangements of
the four things {ba, c, d, e}, which is also 4! or 24.
Answer = 2×24 = 48 ways.
b) c refuses to sit with d.
First we find the number of ways anybody can sit anywhere.
That's the number of arrangements of
the four things {a, b, c, d, e}, which is 5! or 120.
The we subtract from that 5! the number of unwanted arrangements.
The unwanted arrangements are
The number of arrangements of
the four things {a, b, cd, e}, which is 4! or 24.
PLUS
he number of arrangements of
the four things {a, b, dc, e}, which is also 4! or 24.
as that's 2×24 just as in part a),
[so we could have just observed that the number of unwanted
arrangements here was the same as the answer to a), 48]
Answer: 5! - 2×4! = 120 = 2×24 = 120 - 48 = 72
Edwin
