The Student Room Group

Permutation and Combination

Pegs are to be placed in the four holes shown, one in each hole. The pegs come in different colours and pegs of the same colour are identical. Calculate how many different arrangements of coloured pegs in the four holes can be made using
(i) 6 pegs, all of different colours, [1]
(ii) 4 pegs consisting of 2 blue pegs, 1 orange peg and 1 yellow peg. [1]
Beryl has 12 pegs consisting of 2 red, 2 blue, 2 green, 2 orange, 2 yellow and 2 black pegs. Calculate how many different arrangements of coloured pegs in the 4 holes Beryl can make using
(iii) 4 different colours, [1]
(iv) 3 different colours, [3]
(v) any of her 12 pegs.

I need help with part (iv)
I did 6P3*4!/2!=1440.
But the answer is wrong.
Thanks in advance
Reply 1
Original post by 123PC
Pegs are to be placed in the four holes shown, one in each hole. The pegs come in different colours and pegs of the same colour are identical. Calculate how many different arrangements of coloured pegs in the four holes can be made using
(i) 6 pegs, all of different colours, [1]
(ii) 4 pegs consisting of 2 blue pegs, 1 orange peg and 1 yellow peg. [1]
Beryl has 12 pegs consisting of 2 red, 2 blue, 2 green, 2 orange, 2 yellow and 2 black pegs. Calculate how many different arrangements of coloured pegs in the 4 holes Beryl can make using
(iii) 4 different colours, [1]
(iv) 3 different colours, [3]
(v) any of her 12 pegs.

I need help with part (iv)
I did 6P3*4!/2!=1440.
But the answer is wrong.
Thanks in advance


please post some workings
Reply 2
Original post by TeeEm
please post some workings


I need help with part (iv)
6P3*4!/2!= 1440
which is wrong
Reply 3
bump
(I need to look at this question today)
Reply 4
Original post by 123PC
I need help with part (iv)6P3*4!/2!= 1440which is wrong




I got 720 for this part
Reply 5
Original post by TeeEm
I got 720 for this part


That's correct. How did you solve it?
Reply 6
Original post by 123PC
That's correct. How did you solve it?


this is a variant of your question
(I steal questions ....)
it will help you to do yours
Reply 7
Original post by TeeEm
this is a variant of your question
(I steal questions ....)
it will help you to do yours

Thank you!
Reply 8
Original post by 123PC
Thank you!


no worries
Reply 9
you do 6P3 x 6P1 which gives 720
i still dont get it
i still dont get it
Firstly you have to choose 3 colours from 6 colours hence 6C3. if we assume we are going to only use red green and blue we can see that only 3 combinations are possible 1(red red green blue) 2(blue blue red green) 3(green green blue red) which al can be arranged in 4!/2! ways. Therefore 3(4!/2!) X 6C3 = 720

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