Dean Chalmers and Julian Gilbey Solutions for Chapter: Permutations and Combinations, Exercise 8: EXERCISE 5E

Using each digit not more than once, how many even four-digit numbers can be made from the digits $1,2,3,4,5,6$ and $7 ?$

Find how many three-digit numbers can be made from the digits $0,1,2,3$ and $4,$ used at most once each, if the three-digit number: three-digit number: 

must be a multiple of $10$

Find how many three-digit numbers can be made from the digits $0,1,2,3$ and $4,$ used at most once each, if the three-digit number: three-digit number: 

cannot begin with zero.

Five playing cards are randomly selected from a standard deck of $52$ cards. These five cards are shuffled, and then the top three cards are placed in a row on a table. How many different arrangements of three of the $52$ cards are possible?

Seven chairs, $A$ to $G,$ are arranged as shown. In how many ways can the chairs be occupied by $7$ of a group of $12$ people if three particular people are asked to sit on chairs $B,D$ and $F,$ in any order?

A minibus has $11$ passenger seats. There are six seats in a row on the sunny side and five seats in a row on the shady side, as shown in the following diagram.

Find how many ways eight passengers can be arranged in these seats if:

there are no restrictions

A minibus has $11$ passenger seats. There are six seats in a row on the sunny side and five seats in a row on the shady side, as shown in the following diagram.

Find how many ways eight passengers can be arranged in these seats if:

one particular passenger refuses to sit on the sunny side

A minibus has $11$ passenger seats. There are six seats in a row on the sunny side and five seats in a row on the shady side, as shown in the following diagram.

Find how many ways eight passengers can be arranged in these seats if:

two particular passengers refuse to sit in seats that are either next to each other or one directly in front of the other.