# MAT - Paper 2016 - Q2

> Source: https://ollybritton.com/notes/maths/problems/mat/2016/q2/ · Updated: 2021-10-13 · Tags: mat, notes, maths

## 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.

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