Three Marbles With 2 Colors Can Be Aranged

All 12 marbles can be arranged permuted in 12.

Three marbles with 2 colors can be aranged.

And at first we care only about how many ways can we pick a color for that slot right there that first slot. In order to arrive at only those permutations that are distinct division is requi. In how many different ways can these things be arranged in a row. 1 slot 2 slot 3 slot and 4 slots.

Enter your objects or the names of them one per line in the box below then click show me to see how many ways they. Since color are repeating so we use this formula 𝑛 𝑝1 𝑝2 𝑝3. Any one of the three colors could be third and any one of the three colors could be fourth unless the first three marbles are red in which case the fourth marble must be one of the other two colors. Example 15 in how many ways can 4 red 3 yellow and 2 green discs be arranged in a row if the discs of the same colour are indistinguishable.

Each of the 9 3 sets is equally likely to be drawn and 2 3 4 of them are successes so the probability of success is 2 3 4 9 3 24 84 2 7. So we raise three to the fourth power and subtract one to get eighty. Here there are three choices for which purple marble goes with the two blue ones and three choices for which blue marble goes with the two purple ones. Answer by edwin mccravy 18145 show source.

So let s say we have 4 slots here. The same 4 colors we ve picked them in different orders. This is the last question on my homework. A permutation of some number of objects means the collection of all possible arrangements of those objects.

Many of these arrangements are identical because same colored marbles are indistinguishable from one another. They can be numbers letters people colors etc. To build such a set you could pick either of the 2 red marbles any one of the 3 white marbles and any one of the 4 blue marbles so there are 2 3 4 such sets. Total number of discs 4 red 3yellow 2 green n 9.

Now with that out of the way let s think about how many different ways we can pick 4 colors. If the marbles are now unlabelled there are 4 possible labellings for the four white marbles 3 labellings for the three black marbles and 2 for the two red marbles. So each unlabelled order gives rise to 4 3 2 labelled orders. Any one of the three colors could be second.

How many ways can i arrange 10 red marbles 5 white marbles and 6 blue marbles in a row.