Q. 24

# A class consists of 10 boys and 8 girls. Thee students are selected at random. What is the probability that the selected group has (i) all boys? (ii) all girls? (iii) 1 boy and 2 girls? (iv) at least one girl? (v) at most one girl?

Answer :

given: class consisting of 10 boys and 8 girls

formula:

three students are selected at random, total possible outcomes are ^{18}C_{3}

therefore n(S)=^{18}C_{3}

= 816

(i) let E be the event that all are boys

n(E)= ^{10}C_{3}

=120

(ii) let E be the event that all are girls

n(E)= ^{8}C_{3}

=56

(iii) let E be the event that one boy and two girls are selected

n(E)= ^{8}C_{1}^{10}C_{2}=360

(iv) let E be the event that at least one girl is in the group

E= {1,2,3}

n(E)= ^{8}C_{1}^{10}C_{2}+^{8}C_{2}^{10}C_{1}+^{8}C_{3}^{10}C_{0}=696

(v) let E be the event that at most one girl is in the group

E= {0, 1}

n(E)= ^{8}C_{0}^{10}C_{3}+^{8}C_{1}^{10}C_{2}=480

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