Porisma

A hint to get started

Distinguish not-all-together from pairwise separation

A group of fifteen people consists of one pair of sisters, one set of three brothers and ten other people. They are arranged randomly in a line.

(i) Find the probability that the sisters are next to each other.

(ii) Find the probability that the brothers are not all next to one another.

(iii) Find the probability that the sisters are next to each other and the brothers are all next to one another.

(iv) Find the probability that either the sisters are next to each other or the brothers are all next to one another or both.

Instead the fifteen people are arranged in a circle.

(v) Find the probability that the sisters are next to each other.

[2012/II/7]

CJC · Discussion · Question 4

For an inclusive “or”, subtract the case containing both blocks.

Read the worked solution