1. Use the Binomial Theorem to find the 5th term in (x + 2y)⁷

2. How many numbers in the range 1000-9999

(a.) do not contain the same digit 3 times or more?

(b.) end with the digit "4" or begin with the digit "2"?

(c.) end with the digit "4" and begin with the digit "2"?

(d.) have exactly two digits that are 4?

(e.) end in an even digit and have no repeated digits?

Explain why the problems were solved the way they were solved.

How did you choose the steps? What is the logic behind the choices that you made? Use complete sentences, good English, and proper mathematical notation.

**Subject Mathematics Discrete Math**