MAT - Paper 2016 - Q2
Flashcards
2021-10-13
What is the expression for the number of ways you can arrange $AABBB$?
\[\frac{5!}{2! \times 3!}\]
What is the expression for the number of ways you can arrange $AAAABBBCC$?
\[\frac{9!}{4! \times 3! \times 2!}\]
What is the expression for the number of ways you can arrange $A^x B^y C^z …$ (where $x$, $y$ and $z$ denote repetitions)?
\[\frac{(x + y + z)!}{x!y!z!}\]
What’s the fastest way to show one number isn’t divisible by another?
The bus stop method.
If you’re struggling to show one number is divisible by another big-ish number, how could you simplify the problem?
Show that one of the prime factors of the big-ish number doesn’t divide.