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Maths in a minute - combinatorics
And while we're on the topic of probability, let's answer one of those important mathematical question: how likely are you to win the lottery?
In the UK lottery you have to choose 6 numbers out of 49, and for a chance at the jackpot you need all of your 6 numbers to come up in the main draw. So the question is really how many possible combinations of 6 numbers can be drawn out of 49? There are 49 possibilities for the first number, 48 for the second, and so on to 44 possibilities for the sixth number, so there are 49 x 48 x 47 x 46 x 45 x 44 = 10068347520 ways of choosing those six numbers... in that order. But we don't care which order our numbers are picked, and the number of different ways of picking 6 numbers are 6 x 5 x 4 x 3 x 2 x 1 = 6! = 720. Therefore our six numbers are one of 49 x 48 x 47 x 46 x 45 x 44 / 6! = 13983816 so we have about a one in 14 million chance of hitting the jackpot. Hmmm...
But on a brighter note, we have just discovered a very useful mathematical fact: the number of combinations of size k (sets of objects in which order doesn't matter) from a larger set of size n is n! / (n-k)! / k!.
This sort of argument lies at the heart of combinatorics, the mathematics of counting. It might not help you win lotto, but it might keep you healthy. It is used to understand how viruses such as influenza reproduce and mutate, by assessing the chances of creating viable viruses from random recombination of genetic segments.
You can read more on combinatorics, including money (lotto), love (well kissing frogs) and fun (juggling and rubiks cubes) on Plus.
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Are you a winner?
If you're between 11 and 18, live in the UK and have just completed an interesting maths, science, engineering, or technology project, then why not enter the National Science and Engineering Competition?
The best entries will be invited to present their project at the Big Bang: UK Young Scientists’ and Engineers’ Fair, in Manchester in March 2010. You’ll have your own stand to show off all your hard work to over 13,000 scientists, engineers, students, parents, employers, teachers and celebrities. Plus you may even be chosen to face a VIP panel in the competition finals.
There are over £50,000 in prizes up for grabs, including cash awards and trips abroad. And entrants in the senior category could be crowned the UK Young Scientist of the Year or the UK Young Engineer of the Year.
It doesn't matter if your project has already been entered into another competition, you're still eligible, but hurry up, the closing date is October 30th!
The image above shows last year's winners Peter Hatfield (left) and Chris Jefferies (right).
nrich
Stage 2::[problem*] 28 and it's upward and onward
motivate
Motivate...
Mathematically based videoconferences for schools
- live link with a mathematical expert and other participating schools
- enrichment for students of all ages and their teachers
- cross-curricular topics
- highly interactive live videoconference sessions
Our objectives
- to enable schools to be part of the wider mathematical community
- to provide a range of resources on a variety of topics for students of all ages.
- to help schools set up and establish videoconferencing as a means of accessing high quality educational resources
Opportunities for students to:
- understand how maths relates to real life and other curriculum areas
- develop their own maths
- tell other participants about their work
- respond to questions from their peers and an expert
- find out what the others did with the same starting points
Thu, 15 Jan 2009 11:39:46 +0000 motivateadmin 1 at http://motivate.maths.org/content Read more.
nrich
