Question

9. There are 5 girls and 3 boys in a statistics class. A group of 2 girls and 1 boy is to be formed to solve a particular problem. In how many ways can such a group be formed when:
a. Any boy and any girl may be included in the group
b. One particular girl may be included in the group.
c. Two particular girls may be included in the group.
10. The tourism department of a regional government have 5 vacancies of tourist managers to fill out 12 applicants who all are equally qualified for these posts. In how many ways can the vacancies be filled?

Answer 1

Question #15987 9. There are 5 girls and 3 boys in a statistics class. A group of 2 girls and 1 boy is to be formed to solve a particular problem. In how many ways can such a group be formed when:

a. Any boy and any girl may be included in the group

b. One particular girl may be included in the group.

c. Two particular girls may be included in the group.

10. The tourism department of a regional government have 5 vacancies of tourist managers to fill out 12 applicants who all are equally qualified for these posts. In how many ways can the vacancies be filled?.

Solution Solution follows from definition of binomial coefficients.

a) $\binom{5}{2} \cdot \binom{3}{1}$.

b) Now we are only to choose one girl from 4 girls and 1 boy from 3 boys, hence we get $\binom{4}{i} \cdot \binom{4}{1}$.

c) We are only to choose a boy, $\binom{3}{1}$.

10) From definition of binomial coefficient follows that number of ways equals $\binom{12}{5}$.