Dean Chalmers and Julian Gilbey Solutions for Chapter: Permutations and Combinations, Exercise 11: EXERCISE 5G

A farmer has $50$ animals. They have $24$ sheep, of which three are male, and they have $26$ cattle, of which $20$ are female. A veterinary surgeon wishes to test six randomly selected animals. Find the probability that the selection consists of:

more females than males.

How many distinct arrangements of the letters in the word $\mathrm{STATISTICS}$ are there?

Letters in the word $\mathrm{STATISTICS}$ are arranged distinctly. Find the probability that a randomly selected arrangement begins with three $Ts$.

Letters in the word $\mathrm{STATISTICS}$ are arranged distinctly. Find the probability that a randomly selected arrangement begins with three identical letters.

Three skirts, four blouses and two jackets are hung in random order on a clothes rail. Find the probability that:

the three skirts occupy the middle section of the arrangement

Three skirts, four blouses and two jackets are hung in random order on a clothes rail. Find the probability that:

the two iackets are not separated.

In a group of $180$ people, there are $88$ males, nine of whom are left-handed, and there are $85$ females who are not left-handed. If six people are selected randomly from the group, find the probability that exactly four of them are left-handed or female.

A netball team of seven players is to be selected at random from five men and $10$ women. Given that at least five women are selected for the team, find the probability that exactly two men are selected.