Suppose you are asked to list, in order of preference, your five favorite albums you purchased in the past 12 months. if you bought 20 albums over this time period, in how many ways can the five favorites be ranked?

When the order doesn't matter, we would be using the Combination. While, when the order does matter it is called permutation.

In this case, permutation would be use since there is a ranking for the albums.

We need to choose and arrange 5 albums out of 20. Hence, the number of possible ways will be:

5/20 P = 20! Divided by (20 – 5)! = 20 x 19 x 18 x 17 x 16 = 1860480

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."