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)

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.