Three Marbles With 2 Colors Can Be Aranged

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.

Three marbles with 2 colors can be aranged. So we raise three to the fourth power and subtract one to get eighty. 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.

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. 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. Now with that out of the way let s think about how many different ways we can pick 4 colors. Many of these arrangements are identical because same colored marbles are indistinguishable from one another.

Any one of the three colors could be first. 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. How many ways can i arrange 10 red marbles 5 white marbles and 6 blue marbles in a row. 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.

Fracisco s game involves 3 green 2 yellow 4 red and 3 black marbles. Answer by edwin mccravy 18145 show source. 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. So let s say we have 4 slots here.

The same 4 colors we ve picked them in different orders. 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. 1 slot 2 slot 3 slot and 4 slots. All 12 marbles can be arranged permuted in 12.

Any one of the three colors could be second. A permutation of some number of objects means the collection of all possible arrangements of those objects. 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.

So each unlabelled order gives rise to 4 3 2 labelled orders.