+498 I have $4$ different mathematics textbooks and $3$ different psychology textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if all the psychology textbooks are together?
+2159
I have $4$ different mathematics textbooks and $3$ different psychology textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if all the psychology textbooks are together?
Strap the psychology books together and consider it as a single unit.
Along with the 4 math books, and the strapped books we have 5 items.
Five items can be grouped 5P5 ways, aka 5 factorial, which is 120 ways.
But wait. The psychology books could have been grouped several different ways.
In fact, the psych books can be grouped 3P3 ways, aka 3 factorial, which is 6 ways.
In total, keeping the psych books together, the books can be placed (120) • (6) = 720 ways.
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