Classroom

Of the 26 pupils in the classroom, 12 boys and 14 girls, four representatives are picked to the odds of being:
a) all the girls
b) three girls and one boy
c) there will be at least two boys

Correct result:

p1 =  0.067
p2 =  0.2922
p3 =  0.6409

Solution:

p1=14 13 12 1126 25 24 23=771150=0.067p_{1}=\dfrac{ 14 \cdot \ 13 \cdot \ 12 \cdot \ 11 }{ 26 \cdot \ 25 \cdot \ 24 \cdot \ 23 }=\dfrac{ 77 }{ 1150 }=0.067
C3(14)=(143)=14!3!(143)!=141312321=364  C1(12)=(121)=12!1!(121)!=121=12  C4(26)=(264)=26!4!(264)!=262524234321=14950  p2=(143) (121)/(264)=364 12/14950=168575=0.2922
p3=1p1p2=10.0670.2922=7371150=0.6409



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