1991 HSC 3U perms and combs (2 Viewers)

[asianese]

Just wanted to check my logic.

4c)

Containers are coded by different arrangements of coloured dots in a row. The colours used are red, white, and blue.

In an arrangement, at most three of the dots are red, at most two of the dots are white, and at most one is blue.

i) Find the number of different codes possible if six dots are used.

ii) On some containers only five dots are used. Find the number of different codes possible in this case. Justify your answer.



i)
If we use 6 then we must use the maximum of all the dots. So the total is since the reds and whites are identical and they repeat.

ii)
For 5, consider the following cases:

1. 3 red, 2 white =
2. 3 red, 1 white, 1 blue =
3. 2 red, 2 white, 1 blue =

Hence the total is 60 for 5 dots.

Thanks!

 

[deswa1]

Just wanted to check my logic.

4c)

Containers are coded by different arrangements of coloured dots in a row. The colours used are red, white, and blue.

In an arrangement, at most three of the dots are red, at most two of the dots are white, and at most one is blue.

i) Find the number of different codes possible if six dots are used.

ii) On some containers only five dots are used. Find the number of different codes possible in this case. Justify your answer.



i)
If we use 6 then we must use the maximum of all the dots. So the total is since the reds and whites are identical and they repeat.

ii)
For 5, consider the following cases:

1. 3 red, 2 white =
2. 3 red, 1 white, 1 blue =
3. 2 red, 2 white, 1 blue =

Hence the total is 60 for 5 dots.

Thanks!

Yep. Haha just did this EXACT question in Cambridge except with different coloured dots lol. Both answers are right

 

[Siddy123]

h8 dis topic... but yeah asianeyes yoo right

 

[Sy123]

Yup that seems about right I would think (would someone confirm)