HW1. MA3160. Due 09/09/2021

Suppose a License plate must consist of a combination of 8 numbers or letters. How many license plates are there if:
1. there can only be letters?
2. the first three places are numbers and the last five are letters?
3. the first four places are numbers and the last four are letters, but there can not be any repetitions in the same license plate?
A school of 60 students has awards for the top math, English, history and science student in the school
1. How many ways can these awards be given if each student can only win one award?
2. How many ways can these awards be given if students can win multiple awards?
An iPhone password can be made up of any 6 digit combination.
1. How many different passwords are possible?
2. How many are possible if all the digits are odd?
Suppose you are organizing your textbooks on a book shelf. You have three chemistry books, 5 math books, 5 history books and 5 English books.
1. How many ways can you order the textbooks if you must have math books first, English books second, chemistry third, and history fourth?
2. How many ways can you order the books if each subject must be ordered together?

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