Someone trips on the sidewalk, droppingan urn containing 3 blue and 3 yellow marbles. themarbles roll away, but come to a stop (all in a row) on a crack in the cement. What is the probabilityof the three blue marbles ending up next to one an-other (i. e., without any yellow marbles in betweenthem)

Question

Mathematics

Franco Orozco

10 August, 20:19

Someone trips on the sidewalk, droppingan urn containing 3 blue and 3 yellow marbles. themarbles roll away, but come to a stop (all in a row) on a crack in the cement. What is the probabilityof the three blue marbles ending up next to one an-other (i. e., without any yellow marbles in betweenthem)

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Jonathan Day · Answer 1

The probability of the three blue marbles ending up next to one another (i. e., without any yellow marbles in between them is 1/5 or 0.2.

Step-by-step explanation:

The 6 marbles can be arranged in 6! ways, But, there are 3 identical marbles of similar colour in two separate cases,

So, 6 marbles, consisting of 3 blue and 3 yellow marbles can be arranged in 6! / (3!3!) ways = 20 ways.

But, to arrange the six marbles in such a way that the 3 blue marbles end up next to one another without any yellow marble between them. This can be done by viewing the 3 blue marbles as one. Therefore, there are 4 marbles; 3 identical, blue marbles and 1 special marble.

To arrange that, it is, 4! / (3!1!) = 4

The probability of the three blue marbles ending up next to one another (i. e., without any yellow marbles in between them will be 4/20 = 1/5 or 0.2.