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 Maths Question 20
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By: shirley wee (offline)  Sunday, July 29 2012 @ 12:00 AM CDT (Read 759 times)  
shirley wee

Oh no! I am so confused with this question. Can someone help me?

Jason arranged five coloured vases, red, blue, yellow, green and pink, in the sam row, one behind the other. He did not place the pink and red vases behind or in front of each other as they were of similar shade of colour. He placed the pink vase at the end of the row as it as the tallest vase. How many different ways could Jason arrange the vases?

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By: JessicaTan (offline)  Sunday, July 29 2012 @ 02:37 AM CDT  

Hi shirley wee,
I do apologize if I am wrong. Do let me know again if this does not match your answerkey.
For question 20, the final answer is 12 ways.
As the pink vase must be at the back all the time, you could this way:
You can put vase R at the top first like this : (In sam row )
Starting with 'R' : R,B,Y,G,P. (1st way) R,Y,B,G,P (2nd way) R,Y,G,B,P(3rd way)
Starting with 'B' : B,R,Y,G,P (4th way) B,Y,R,G,P (5th way) B,G,R,Y,P (6th way)
Starting with 'Y' : Y,B,R,G,P (7th way) Y,R,B,G,P (8th way) Y,G,R,B,P (9th way)
Starting with 'G' : G,B,R,Y,P (10th way) G,R,B,Y,P(11th way) G,Y,R,B,P(12th way)

That is the solution of how I did it. There is no 'P' as it is at the back all the time.
Switch the letters around (without making 'P' moving up) and you can get 12
ways too.
Once again, I do apologize if I am wrong with the answer. Smile

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By: chloee (offline)  Sunday, July 29 2012 @ 03:32 AM CDT  

i think there are some other ways :
as the permutation of 3! is 6 :
starting with 'R' : RBYGP (1st way), RBGYP (2nd), RYBGP, RYGBP, RGBYP, RGYBP (6th way)
starting with 'B': BRYGP,BRGYP, BYRGP,BGRYP (only 4 ways as Red would not be placed in front of Pink)
starting with 'Y' : 4 ways like 'B'
starting with 'G' : 4 ways like 'B'
so total 18 ways

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