Two students are asked to find how many ways there are to plant two trees and three bushes in a row. The first student gives $5!=120,$ and the second gives $\frac{5!}{2!\times 3!}=10.$ Decide who you agree with and explain the error made by the other student.

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.

Find how many five-digit numbers can be made using the digits $2,3,4,5$ and $6$ once each if:

there are no restrictions