Dean Chalmers and Julian Gilbey Solutions for Chapter: Permutations and Combinations, Exercise 9: EXERCISE 5F

A girl has $11$ objects to arrange on a shelf but there is room for only seven of them. In how many ways can she arrange seven of the objects in a row along the shelf, if her clock must be included?

A Mathematics teacher has $10$ different posters to pin up in their classroom but there is enough space for only five of them. They have three posters on algebra, two on calculus and five on trigonometry. In how many ways can they choose the five posters to pin up if:

there are no restrictions

A Mathematics teacher has $10$ different posters to pin up in their classroom but there is enough space for only five of them. They have three posters on algebra, two on calculus and five on trigonometry. In how many ways can they choose the five posters to pin up if:

they decide not to pin up either of the calculus posters

A Mathematics teacher has $10$ different posters to pin up in their classroom but there is enough space for only five of them. They have three posters on algebra, two on calculus and five on trigonometry. In how many ways can they choose the five posters to pin up if:

they decide to pin up at least one poster on each of the three topics algebra, calculus and trigonometry?

Each letter $A$ to $Z$ is encrypted (or transformed) to a fixed distinct letter using its position in the alphabet $(\mathrm{A}=1, \mathrm{B}=2,\mathrm{C}=3,\dots ).$ By doing this, the password $\mathrm{SATURN}$ is encrypted as $\mathrm{ECHKBP}$. Similarly the encrypted password for a word is $\mathrm{UJSNOL}$. Find the number of possibilities for the original word.

How many distinct three-digit numbers can be made from $1,2,2,3,4$ and $5,$ using each at most once?

From three sets of twins and four unrelated girls, find how many selections of five people can be made if exactly:

two sets of twins must be included

From three sets of twins and four unrelated girls, find how many selections of five people can be made if exactly:

one set of twins must be included.