1) In how many ways can 6 boys be arraned in a line? 2) In how many ways can 6 b
ID: 2913574 • Letter: 1
Question
1) In how many ways can 6 boys be arraned in a line? 2) In how many ways can 6 boys be arraned in a circle?1) 6 boys can be arranged in a line in 6! ways = 6*5*4*3*2*1 =720 2) 6 boys can be arranged in a circle in (6-1)! ways = 5! = 5* 4 * 3 * 2 * 1 =120 Why do you use 6! for the line and (6-1)! for the circleformation? 1) In how many ways can 6 boys be arraned in a line? 2) In how many ways can 6 boys be arraned in a circle?
1) 6 boys can be arranged in a line in 6! ways = 6*5*4*3*2*1 =720 2) 6 boys can be arranged in a circle in (6-1)! ways = 5! = 5* 4 * 3 * 2 * 1 =120 1) 6 boys can be arranged in a line in 6! ways = 6*5*4*3*2*1 =720 2) 6 boys can be arranged in a circle in (6-1)! ways = 5! = 5* 4 * 3 * 2 * 1 =120 Why do you use 6! for the line and (6-1)! for the circleformation?
Explanation / Answer
This is different to 6 people in a line, because the 6 people ina circle can ALL move one (or more)places to the left/right, without affecting the order of seating.In other words, A B C D E F, B C D E F A, C D E F A B, etc., areALL the same circulararrangement because they have the same order. (We do notcount arrangements that are the same as a previous one, eventhough the order might fall in a different position. That is why you have to subtract 1 from your total number ofpossible operations.)
Because they are in a line, you cannot move all at thesame time and reach the same order ever. That iswhy there would be 6! = 720 possiblearrangements.
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