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Aliun [14]
2 years ago
12

A bag contains ten identical blue marbles and ten identical green marbles. In how many distinguishable ways can five of these ma

rbles 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
Mathematics
1 answer:
ivann1987 [24]2 years ago
7 0

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

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