# Factorials

### Zero factorial

0! = 1

Dr James Grime tries to explain why this is the case

### 10! Numberphile

Ten factorial is 10x9x8x7x6x5x4x3x2x1 - or six weeks!

Featuring Dr James Grime, aka singingbanana.

### 69! Numberphile

69 is the largest number that most hand-held calculators can factorialize!

Professor Laurence Eaves from the University of Nottingham explains.

### How many ways can you arrange a deck of cards?

One deck. Fifty-two cards. How many arrangements? Let's put it this way: Any time you pick up a well shuffled deck, you are almost certainly holding an arrangement of cards that has never before existed and might not exist again. Yannay Khaikin explains how factorials allow us to pinpoint the exact (very large) number of permutations in a standard deck of cards.

### Combinations and Pascal's Triangle

Combinations consists of seven instant maths ideas including a consideration of the number of arrangements of dots used when writing in Braille, an investigation of Pascal’s triangle, investigating the number of routes through New York, exploring the number of ways six letters can incorrectly be placed in six envelopes.

Other activities explore the formula for calculating the number of combinations relating the results to numbers found in Pascal’s triangle. Understanding of factorial is required for this section.

### Properties of Number

Squares and Primes is a booklet investigating prime numbers, primes and factorials, proof, Euclid and Greek mathematics.

### Algebra

A simple sheet explaining what is meant by a factorial.

### Maths Made Magic

This handbook of magical mathematical tricks is intended for use in the classroom to help teach many of the basic concepts in mathematics in an engaging and entertaining way. The tricks have been mapped to topics found in Key Stage Four and are as diverse as Pythagoras' theorem, simultaneous equations, probability, sine and cosine, factors, loci, powers and indices, vectors, ratios, factorials and many more.

Accompanying each trick is a comprehensive description of how the trick is to be performed, what effect is attempting to be achieved and the mathematics behind why the illusion works.The book contains photocopiable resources for use with the tricks.

### Number and Algebra Mixed

Number and algebra mixed pack four contains eleven work cards with activities including ordering fractions, decimals and directed numbers, estimating solutions to calculations, using a calculator to solve problems using trial and improvement, a number of games involving powers, roots and factorials, and using the log button on a calculator.