Domain and Range

Following on from the year twelve lessons this week, here are some supporting materials on domain and range.

First of all, a clear and concise video explaining domain and range:

Next a link to some notes and examples on Domain and Range.

Finally a link to an activity for finding the domain and range of a function using its graph.

The difference between perms and combs

This post is in response to a question that I was asked in my 12C Stats class. The question was why do we use combinations in working out probabilities in the binomial distribution and not permutations.

Imagine that there is a squad of twenty footballers. The number of ways of selecting a team of eleven is 20C11.

However, if you care whether the goalie goes in goal or up front on the left then the order is important. So we use 20P11 to find all the different positions that the players could play in.

In the case of selecting 5 spades from 10 decks of cards, the order in which we lay the cards on the table, their position, is unimportant. Only which decks they came from is important. So we use 10C5.

When we want to work out the probability of selecting 5 spades then we take the number of combinations of 5 spades from ten decks and multiply it by the probability of selecting 5 spades and 5 non-spades.

Hence
X~Bin(10,1/4)
Pr(X=5)=10C5 x (1/4)^5 x (3/4)^5
=252 x 0.0009765625 x 0.237304688
=0.0584 (3sf)

I hope this helps.