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?

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  Rate this question :

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