Three Marbles With 2 Colors Can Be Aranged

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Three marbles with 2 colors can be aranged.

How many ways can i arrange 10 red marbles 5 white marbles and 6 blue marbles in a row. Answer by edwin mccravy 18145 show source. Any one of the three colors could be first. In how many different ways can these things be arranged in a row.

Many of these arrangements are identical because same colored marbles are indistinguishable from one another. If he randomly draws three marbles from the bag without replacement what is the probability that he will draw yellow and then red and then black. And at first we care only about how many ways can we pick a color for that slot right there that first slot. Total number of discs 4 red 3yellow 2 green n 9.

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. They can be numbers letters people colors etc. Now with that out of the way let s think about how many different ways we can pick 4 colors. Any one of the three colors could be second.

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. The same 4 colors we ve picked them in different orders. In order to arrive at only those permutations that are distinct division is requi. 1 slot 2 slot 3 slot and 4 slots.

All 12 marbles can be arranged permuted in 12. 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. So each unlabelled order gives rise to 4 3 2 labelled orders. 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.

So let s say we have 4 slots here. 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. Since color are repeating so we use this formula 𝑛 𝑝1 𝑝2 𝑝3. This is the last question on my homework.

Fracisco s game involves 3 green 2 yellow 4 red and 3 black marbles.