<span lang=

given: class consisting of 10 boys and 8 girls

formula:

three students are selected at random, total possible outcomes are ¹⁸C₃

therefore n(S)=¹⁸C₃

= 816

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

n(E)= ¹⁰C₃

=120

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

n(E)= ⁸C₃

=56

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

n(E)= ⁸C₁¹⁰C₂=360

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

E= {1,2,3}

n(E)= ⁸C₁¹⁰C₂+⁸C₂¹⁰C₁+⁸C₃¹⁰C₀=696

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

E= {0, 1}

n(E)= ⁸C₀¹⁰C₃+⁸C₁¹⁰C₂=480