The numbers $1, 2, 3, 4, 5$ are to be arranged in a circle. An arrangement is bad if it is not true that for every $n$ from $1$ to $15$ one can find a subset of the numbers that appear consecutively on the circle that sum to $n.$ Arrangements that differ only by a rotation or a reflection are considered the same. How many different bad arrangements are there?

Let $8$ persons can be seated on a round table, then the number of ways

(a) are $M$, if two of them (say $A$ and $B$) must not sit in adjacent seats.

(b) are $N$, if $4$ of the persons are men and $4$ ladies and if no two men are to be in adjacent seats.

(c) are $P$, if $8$ persons constitute $4$ married couples and if no husband and wife, as well as no two men are to be in adjacent seats.

Find the value of $\left(\frac{M-N}{10P}\right)$.