Discrete Mathematics
# Bijections

Suppose that \(10\) dice are rolled. Each die is a regular \(6\)-sided die with numbers \(1\) through \(6\) labelled on the sides. How many different distinct sums of all 10 numbers are possible?

**Details and assumptions**

The sums \(5 = 1+4 \) and \(5 = 2 + 3 \) are the same sum (namely 5), and should only be counted once.

Suppose that \(10\) dice are rolled. Each die is a regular \(6\)-sided die with numbers \(1\) through \(6\) labelled on the sides. How many different distinct sums of all 10 numbers are possible?

**Details and assumptions**

The sums \(5 = 1+4 \) and \(5 = 2 + 3 \) are the same sum (namely 5), and should only be counted once.

Mary has enrolled in \(6\) courses: Chemistry, Physics, Math, English, French and Biology. She has one textbook for each course and wants to place them on a shelf. How many ways can she arrange the textbooks so that the English textbook is placed before the French textbook?

**Details and assumptions**

If the books are ordered from left to right, then the "English textbook is placed before the French textbook" means that the English textbook was placed to the left of the French textbook. They do not need to be immediately beside each other.

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