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[學科討論] 數學問題

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數學問題

(a) How many ways to distribute 10 books to 4 boys (note that the books are different)?
(b) How many ways to distribute 10 books to 4 boys so that the oldest boy gets 4 books and the other two boys get 2 books each?
(c) How many ways to distribute 10 candies to 4 boys (note that the candies are indistinguishable)?
(d) How many ways to distribute 10 candies to 4 boys so that the oldest boy gets at least 2 candies and every boy gets at least one candy?
   

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(a) There are 4 options for the owner of each book, so the total ways = 4 x 4 x ...
(b) Denote the four boys be A, B, C and D. Take A as the oldest boy, give 4 books to A first, then 2 to B, 2 to C and the remaining 2 to D. Order of the books does not matter.
(c) Hint: 1 + 1 + 1 + 7 = 10, 0 + 0 + 0 + 10 = 10, ... , the message here is the "+".
(d) The problem can be simplified to sharing 5 candies among 4 boys. Why?
mtutor15@App 17

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