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發問:
1.John and Amy invite 6 friends to their party. The 8 participants are arranged in 2 rows of 4 in order to take a photograph. Find the number of arrangements that can be made if John and Amy are next to each other.2. 5 men and 4 women join a social evening. There are a round table of 4 seats and a table of 5... 顯示更多 1.John and Amy invite 6 friends to their party. The 8 participants are arranged in 2 rows of 4 in order to take a photograph. Find the number of arrangements that can be made if John and Amy are next to each other. 2. 5 men and 4 women join a social evening. There are a round table of 4 seats and a table of 5 seats for them. In how many ways can they be seated if there is at least 1 women sitting at the round table of 5 seats?
最佳解答:
1) The number of arrangement Ans: 360 (a)撇除John and Amy,先從6人中抽出4人排成一行:C(6)(4) (b)將John and Amy 當成1組人,二人可以左右換轉:2 (c)餘下2人與John and Amy排成一行:3! (d)上下排可以換轉:2 where C = Combination, 3! = 3x2x1 The number of arrangement C(6)(4) x 2 x 3! x 2 = (6!)/(4!)[(6-4)!] x 24 = 15 x 24 = 360 The number of arrangement is 360. 2) Number of ways they can be seated Ans: 40,320 (a)先從4個女人中選1人在5人枱:C(4)(1) (b)在餘下8人中選4人在5人枱:C(8)(4) (c)5人枱座位安排的可能性:(5-1)! (d)4人枱座位安排的可能性:(4-1)! where C = Combination, 4! = 4x3x2x1 Number of ways they can be seated C(4)(1) x C(8)(4) x (5-1)! x (4-1)! = (4!)/(3!)[(4-3)!] x (8!)/(4!)[(8-4)!] x 4! x 3! = 4 x 70 x 24 x 6 = 40,320 There are 40,320 ways they can be seated.
其他解答:7638E7481407D16B