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

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

the five-digit number must be odd.

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

the five-digit number must be even.

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

the five-digit number must be odd and less than $40000.$