Students are given a list of ten vocabulary words to learn. In how many ways could four of the words be listed on a test?
10*4
40 ways
There are ten ways the first book can be placed, nine ways the second, eight ways the third,...
10*9*8*7 or
10!/(10-4)!
so 5040 ways? that's a lot
To determine the number of ways four words can be listed on a test from a list of ten vocabulary words, we can use the concept of combinations. The formula for combinations is given as:
𝐶(𝑛, 𝑟) = 𝑛! / (𝑟!(𝑛−𝑟)!)
In this case, we want to select four words from a list of ten, so we can calculate it as:
𝐶(10, 4) = 10! / (4!(10−4)!)
Simplifying this expression:
𝐶(10, 4) = 10! / (4! * 6!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210
Therefore, there are 210 different ways four words can be listed on the test from the given list of ten vocabulary words.