Is $3! + 4! = 7!$?

All possible four-digit numbers are formed using the digits $0, 1, 2, 3$ such that no digit is repeated. The number of even numbers among them is

How many $2$ digit even numbers can be formed from the digits $1, 2, 3, 4, 5$ if the digits can be repeated?

How many $5$-digit telephone numbers can be constructed using the digits $0$ to $9$ if each number starts with $67$ and no digit appears more than once?

Evaluate $\frac{n!}{(n-r)!}$ when $n=6$ and $r=2$.

How many ways are there to arrange the letters of the word $EDUCATION$ so that all the following three conditions hold?
- The vowels occur in the same order $(E, U, A, I, O)$.
- The consonants occur in the same order $(D, C, T, N)$.
- No two consonants are next to each other.