Help with Perm + Comb question (1 Viewer)

[Skinnysweatyman]

Hi guys. i have no idea how to do these two questions.

1. There are three identical blue marbles and four identical yellow arranged in a row. How mand different arrangements of 5 marbles are possible?


2. Containers are coded by different arrangements of coloured dots in a row. The colours used a red, white and blue.
In an arrangement, at most three of the dots are red, at most two are white and at most one is blue.

How many different codes possible using 5 dots?



thx guys, i have no idea

 

[Skinnysweatyman]

Well i figured them out so i'll post my answers in case anyone else was having trouble.

1. because there are only two options (b/y) you could rewrite that as blue and notblue. Then, because there are only 3 blues maximum, you just work out:

(no of combinations using 1b) + (no of combs using 2b) + no of combs using 3b)

OR

5C1 + 5C2 + 5C3 = 25


2. using 5 dots, you will only really have three options.

(2red, 2white and 1blue) + (3r, 1w and 1b) + (3r, 2w)

OR

(5! / 2!.2!.1!) + (5! / 3!.1!.1!) + (5! / 3!.2!) = 60