概率的問題抽球

概率的問題抽球

[匿名]

2013-01-26 12:48 am

1. Calculate the amount of possible telephone numbers in total, if telephone numbers are 8-digit and “00”, “999”, “128100” are reserved for special numbers. (Hints:
think of how you dial telephone numbers in practice.)

2. Suppose we want to distribute 10 balls into 4 boxes. The balls are the same, while
the boxes are numbered.
(a) How many ways to distribute the balls, if each box has at least 1 ball?
(b)How many ways to distribute the balls, if a box can receive 0 ball?

回答 (1)

用戶9112

2013-01-26 5:27 am

✔ 最佳答案

(1) The total amount of all 8 digit numbers = 10 ×10×10×10×10×10×10×10
= 100000000Forbidden numbers are 00XXXXXX, 999XXXXX and 128100XXThe amount of forbidden numbers
= 1000000 + 100000 + 100 = 1100100Hence the total amount of possible telephone numbers
= 100000000 – 1100100 = 98899900(2)(a) First put 1 ball in each of the boxes so there are 6 balls remaining to be distributedTo distribute 6 balls among 4 boxes is equivalent to arranging the 6 balls in a row with 3 separatorsO|OO|O|OO, i.e.to determine 3 separator positions out of a total of 9.The total number of methods = C(6+3,3) = C(9,3) = 84 ways(b) To distribute 10 balls to 4 boxes, there are C(10+3,3) = 286 ways

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概率的問題 抽球

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