Permutations or Combination?

chan

2009-09-28 2:51 am

1)How many numbers can be formed from the digits1,2,3,and 4
if repetitions are not allowed?(note:42 and 231 are examples of such numbers.)

2)Determine the number of positive integers less than 10,000 that can br formed from the digits 1,2,3,and 4 if repetitions tions are allowed.

3)suppose you toss a fair coin 5 times. Find the number of the
different ways to observe 5 heads and 2 tails.

可唔可以連埋解釋?
thz~^^

更新1:

can be formed

更新2:

SORR..我第3題打錯係 3 heads and 2 tails....

回答 (1)

用戶2053

2009-09-28 6:13 am

✔ 最佳答案

1) For 1 digit numbers : 4C1 = 4 numbers
For 2 digits numbers : 4C2 * 2! = 12 numbers
For 3 digits numbers : 4C3 * 3! = 24 numbers
For 4 digits numbers : 4C4 * 4! = 24 numbers
Total : 4 + 12 + 24 + 24 = 64 numbers can be formed.
2) 4 + 4^2 + 4^3 + 4^4 = 4(1 - 4^4) / (1 - 4) = 340 numbers can be formed.
3)Toss 5 times is impossible to observe 5 heads and 2 tails.
I guess your question is toss a fair coin 7 times :
7C5 or 7C2 = 21 ways.
Or 7! / (5! * 2!) = 21 ways.

2009-09-27 23:05:30 補充：
3) (3 heads and 2 tails)

5C3 or 5C2 = 10 ways

Or 5! / (3! * 2!) = 10 ways

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