Answer to Question #264441 in Statistics and Probability for Myla Fajji

Question

In how many ways can 3 boys and 2 girls sit in a row? In how many ways can they sit in a row if the boys and girls are each to sit together? In how many ways can they sit in a row if just the girls are to sit together?

Answer 1

1) We can estimate how many ways of giving 3 places of 5 for 3 bays(other two place in each situituion will be automatically taken by girl). It is equal to ${5 \choose 3} = 10$ ways.

If we considering that all of the boys and girls are different, than we have 5 ways to place someone on the first place, 4 ways to place someone on the second place etc. The total amount of ways is equal to the amount of permutations without replacement between 5 people

P(5) = 5! = 120

2) there is only 2 such ways: ggbbb, bbbgg(b means boy, g means girl). If we considering every boy and girl are different, then we should find the number of permutations between girls and boy in every situation.

For two girls there is 2! = 2 permutations

For three boys there is 3! = 6 permutations

For each of the two situations there are 2 * 6 = 12 ways, which give us 2 * 12 = 24 ways in total

3) There is 5 - 1 = 4 such ways: ggbbb, bggbb, bbggb, bbbgg. If we considering every boy and girl are different, then we should find the number of permutations between girls and boy in every situation.

For two girls there is 2! = 2 permutations

For three boys there is 3! = 6 permutations

For each of the four situations there are 4 * 6 = 24 ways, which give us 2 * 24 = 48 ways in total