A bag contains ten identical blue marbles and ten identical green marbles. In how many distinguishable ways can five of these marbles be put in a row if there are at least two blue marbles in the row and every blue marble is next to at least one other blue marble

Question

Mathematics

Winston Osborn

28 January, 07:31

A bag contains ten identical blue marbles and ten identical green marbles. In how many distinguishable ways can five of these marbles be put in a row if there are at least two blue marbles in the row and every blue marble is next to at least one other blue marble

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Answers (1)

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Deandre Mcdowell · Answer 1

Answer: 11 different rows.

Step-by-step explanation:

As the marbles are identical, we do not really care for permutations (as we can really not difference them)

If we have 5 blue marbles, we have only one combination.

B-B-B-B-B

If we have 4 blue marbles, we have 3 combinations:

B-B-B-B-G, G-B-B-B-B, B-B-G-B-B

This is because the blue marbles need to be next to another blue one, so from here we can do the same analysis.

If we have 3 of them, we have 3 combinations.

B-B-B-G-G, G-B-B-B-G, G-G-B-B-B

If we have 2 of them, we have 4 combinations

B-B-G-G-G, G-B-B-G-G, G-G-B-B-G, G-G-G-B-B

then we have 1 + 3 + 3 + 4 = 11 combinations