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

A girl has $20$ plastic squares. There are five identical red squares, seven identical blue squares and eight identical green squares. By placing them in a row, joined edge-to-edge, find how many different arrangements she can make using:

the five red squares only

A girl has $20$ plastic squares. There are five identical red squares, seven identical blue squares and eight identical green squares. By placing them in a row, joined edge-to-edge, find how many different arrangements she can make using:

all of the blue and green squares

Ten coins are placed in a row on a table, each showing a head or a tail.

How many different arrangements of heads and/or tails are possible?

Ten coins are placed in a row on a table, each showing a head or a tail.

Find how many arrangements have five heads and five tails showing.

Ten coins are placed in a row on a table, each showing a head or a tail.

Of the total arrangements, find how many have more heads than tails showing.

Find the number of distinct five-letter arrangements that can be made from:

two $As$ and three $Bs$

Find the number of distinct five-letter arrangements that can be made from:

two identical vowels and three $Bs$

Find the number of distinct five-letter arrangements that can be made from:

Two identical vowels and any three identical consonants.