標題:
permutations and combinations
發問:
There are 4 black marbles and 4 white marbles in a bag. 2 points will be awarded if a black marble is drawn and 1 point will be awarded if a white marble is drawn. If 4 marbles are drawn, find the number of ways to obtain at least 6 points.my answer which is incorrect is as follows: case 1) 4 Black =... 顯示更多 There are 4 black marbles and 4 white marbles in a bag. 2 points will be awarded if a black marble is drawn and 1 point will be awarded if a white marble is drawn. If 4 marbles are drawn, find the number of ways to obtain at least 6 points. my answer which is incorrect is as follows: case 1) 4 Black = 4C4 = 1 case 2) 3 Black 1 White = 4C3 x 4C1 = 16 case 3) 2 Black 2 White = 4C2 x 4C2 = 36 1+16+36 = 53 can someone give the correct answer and explain why my answer is wrong ? Thanks.
最佳解答:
會唔會係: 1 + 16 x 4 + 36 x 6 = 281 ? 上面果3個CASES 無錯亦無漏，但係3 Black 1 White , 有可能係第一粒係白，或者第二、三、四粒係白都得，所以要 X 4. 簡單黎講就係你數漏左果4粒波子的Permutation 方式 2013-11-28 14:16:59 補充： 睇錯左~~~ 應該係 1 + 4 + 6 = 11 ways 呢條不是問probability , don't need to Combination skill to select 4 balls out of 8. 只用Permutation to arrange the four letters : BBBB --> 1 way BBBW --> 4 ways BBWW --> 6 ways
其他解答:
permutations and combinations
發問:
There are 4 black marbles and 4 white marbles in a bag. 2 points will be awarded if a black marble is drawn and 1 point will be awarded if a white marble is drawn. If 4 marbles are drawn, find the number of ways to obtain at least 6 points.my answer which is incorrect is as follows: case 1) 4 Black =... 顯示更多 There are 4 black marbles and 4 white marbles in a bag. 2 points will be awarded if a black marble is drawn and 1 point will be awarded if a white marble is drawn. If 4 marbles are drawn, find the number of ways to obtain at least 6 points. my answer which is incorrect is as follows: case 1) 4 Black = 4C4 = 1 case 2) 3 Black 1 White = 4C3 x 4C1 = 16 case 3) 2 Black 2 White = 4C2 x 4C2 = 36 1+16+36 = 53 can someone give the correct answer and explain why my answer is wrong ? Thanks.
最佳解答:
會唔會係: 1 + 16 x 4 + 36 x 6 = 281 ? 上面果3個CASES 無錯亦無漏，但係3 Black 1 White , 有可能係第一粒係白，或者第二、三、四粒係白都得，所以要 X 4. 簡單黎講就係你數漏左果4粒波子的Permutation 方式 2013-11-28 14:16:59 補充： 睇錯左~~~ 應該係 1 + 4 + 6 = 11 ways 呢條不是問probability , don't need to Combination skill to select 4 balls out of 8. 只用Permutation to arrange the four letters : BBBB --> 1 way BBBW --> 4 ways BBWW --> 6 ways
其他解答:
此文章來自奇摩知識+如有不便請留言告知
Maybe someone can say like this: There are 5 possible outcomes (be careful that they are not with equal chance) 1. 4B 2. 3B1W 3. 2B2W 4. 1B3W 5. 4W Then, the number of ways is 3. (cases 1, 2, 3) 2013-11-27 20:40:49 補充： However, the probability of having at least 6 points is NOT 3/5. It should be 53/[8C4] = 53/70 2013-11-27 20:50:20 補充： Your interpretation is that those balls are all distinct. so your case 2 distinguishes B1B2B3W1 from B2B3B4W3 etc. for 16 cases. However, if all black balls are the same and all white balls are the same, then all your 16 cases are just one case 3B and 1W. It should be this issue.
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