https://mathmanstudio.com/categories/%E6%8E%92%E5%88%97%E7%B5%84%E5%90%88%E8%88%87%E6%A9%9F%E7%8E%87/Recent content in 排列組合與機率 on MathManStudio.comHugozh-TWSat, 25 Oct 2025 21:59:06 +0800https://mathmanstudio.com/posts/114%E9%AB%98%E4%B8%AD%E6%95%B8%E5%AD%B8%E5%AD%B8%E6%B8%AC%E6%95%B8a%E5%96%AE%E9%81%B813%E7%8D%A8%E7%AB%8B%E4%BA%8B%E4%BB%B6%E7%9B%B4%E7%B7%9A%E6%96%B9%E7%A8%8B%E5%BC%8F/Sat, 25 Oct 2025 21:59:06 +0800https://mathmanstudio.com/posts/114%E9%AB%98%E4%B8%AD%E6%95%B8%E5%AD%B8%E5%AD%B8%E6%B8%AC%E6%95%B8a%E5%96%AE%E9%81%B813%E7%8D%A8%E7%AB%8B%E4%BA%8B%E4%BB%B6%E7%9B%B4%E7%B7%9A%E6%96%B9%E7%A8%8B%E5%BC%8F/<p><img loading="lazy" src="https://mathmanstudio.com/wp-content/uploads/2025/06/%E6%88%AA%E5%9C%96-2025-06-01-%E6%99%9A%E4%B8%8A8.43.13-1024x774.png"> <img loading="lazy" src="https://mathmanstudio.com/wp-content/uploads/2025/06/%E6%88%AA%E5%9C%96-2025-06-01-%E6%99%9A%E4%B8%8A8.43.33-1024x586.png"></p> <p>$P(藍\cap1號)＝P(藍)\times P(1號)$</p> <p>$\cfrac{2}{9+k}=\cfrac{5}{9+k}\times \cfrac{6}{9+k}$</p> <p>解得k=6 or -9(取正)</p> <p>Ans:(5)</p> <p>😘<strong>兩獨立事件的交集定義！easy~</strong></p> <p><img loading="lazy" src="https://mathmanstudio.com/wp-content/uploads/2025/10/%E6%88%AA%E5%9C%96-2025-10-25-%E4%B8%8B%E5%8D%886.45.39-1024x233.png"></p> <p>先分別求出兩條直線的Y截點分別為</p> <p>（0,$\cfrac{3a}{2}$）與（0,$\cfrac{4a}{3}$）</p> <p>三角形面積等於</p> <p>$(\frac{3a}{2}-\frac{4a}{3})\times a \times \frac{1}{2}=3$</p> <p>解得a=6 or -6(取正)</p> <p>Ans:(2)</p> <p>🧒🏻<strong>Point:利用斜率與直線上一點即可寫出直線方程式～</strong></p> <p><img loading="lazy" src="https://mathmanstudio.com/wp-content/uploads/2025/10/%E6%88%AA%E5%9C%96-2025-10-25-%E6%99%9A%E4%B8%8A7.22.47-1024x368.png"></p> <p>利用加法原理來分類討論</p> <p>（1）討論歌唱排第三只有小鋼歌與鋼小歌兩種</p> <p>總共有：$2\times5!4!3!$</p> <p>(2)討論歌唱排第二只有鋼歌小與小歌鋼兩種</p> <p>總共有：$2\times5!4!3!$ （當然跟上面一樣）</p> <p>總計4種情形：就是$4\times5!4!3!$囉</p> <p>Ans:(4)</p> <p>😄<strong>單純的利用最原始的加法原理一一羅列即可得分！千萬別用取捨原理做啊～</strong></p> <p><strong>有沒有都學會啊～想問陳偉數學問題讓自己越來越厲害的話請立即加入</strong></p> <p><a href="https://mathmanstudio.com/line-%E6%95%B8%E5%AD%B8%E8%A7%A3%E9%A1%8C%E5%AE%A4">LINE數學解題室</a></p>