Evaluate nine 𝑃 five.
𝑛 𝑃 𝑟 is evaluated by dividing 𝑛 factorial by 𝑛 minus 𝑟 factorial, where 𝑛 𝑃 𝑟 is the number of permutations — in other words, the number of ways of obtaining an ordered subset of 𝑟 elements from a set of 𝑛 elements. In our example, 𝑛 is equal to nine and 𝑟 is equal to five. This means that we can evaluate nine 𝑃 five by dividing nine factorial by nine minus five factorial.
Nine factorial is calculated by multiplying all the integers from nine down to one. Nine minus five is equal to four. Therefore, our denominator is four factorial. This is calculated by multiplying four by three by two and by one. Nine factorial is equal to 362880 and four factorial is equal to 24. Dividing 362880 by 24 gives us 15120.
This means that there are 15120 ways of obtaining an ordered subset of five elements from a set of nine elements. Nine 𝑃 five is equal to 15120.