Question

Ali has 6 books, while Adam has 7 books. How many possible ways can they exchange 4 books with each other?

Answer 1

`535` ways

Explanation:

Ali can choose which `4` of his `6` books to give to Adam in `color(white)("x")_6C_4` ways.

For each of these ways, Adam can give Ali `4` of his `7` books in `color(white)(".")_7C4` ways.

Therefore the number of ways in which this exchange can take place is
`color(white)("XXX")color(white)(".")_6C_4 xx color(white)(".")_7C_4`

`color(white)("XXX")=(6!)/(4!2!) xx (7!)/(4!3!)`

`color(white)("XXX")=(6xx5)/(2xx1) xx (7xx6xx5)/(3xx2xx1)`

`color(white)("XXX")=15 xx 35`

`color(white)("XXX")=525`