Question Video: Applications of the Counting Principle Mathematics • Second Year of Secondary School

Video Transcript

There are six books left in a shop. In how many ways can five people take one book each?

In order to answer this question, we need to use our knowledge of permutations. A permutation is an arrangement of a collection of items with no repetition and where order matters. The notation for this is 𝑛 P 𝑟 where 𝑟 is the number of items we’re selecting and 𝑛 is the number of items in total. We can calculate this using the formula 𝑛 factorial divided by 𝑛 minus 𝑟 factorial.

In this question, there are six books left in the shop, so 𝑛 is equal to six. As five people are taking one book each, 𝑟 is equal to five. We need to calculate six p five. This is equal to six factorial divided by six minus five factorial, which can be simplified to six factorial divided by one factorial. As one factorial is equal to one, we simply need to calculate six factorial. To calculate the factorial of any number, we multiply that number by all the integers below it down to one.

In this question, we need to multiply the integers from six to one. Six multiplied by five is equal to 30. Multiplying this by four gives us 120. Multiplying this by three gives us 360. And multiplying this by two gives us 720. Six factorial is equal to 720. Therefore, this is the number of ways that five people can take one book each from the six books left in the shop. We could have calculated the answer using a scientific calculator. We type six followed by the 𝑛 P 𝑟 button then five and press equals. This gives us an answer of 720. Alternatively, we could have just press six, the factorial button, and equals. Using any of these methods gives us an answer of 720.