+441 I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row?
+1279
I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row?
7 • 6 • 5 • 4 • 3 • 2 • 1 = 5040
Seven books total, so you have 7 choices for the first book.
For each of those choices, you have 6 choices for the second book.
There are 5 choices left for the third book in the row.
et cetera until all of the books are shelved.
The expression for the arrangements can be shown as 7! (called seven factorial).
Another way to express the number of arrangements is 7P7 (called seven permute seven).
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