Question 1050920
For the first pick, with 12 females out of 22 students,
the probability of picking one female is {{{12/22}}} .
After that, for the second pick, with 10 males out of 21 available students,
the probability of picking one male is {{{10/21}}} .
After that second pick, you are left with {{{22-2=20}}} students, including {{{10-1=9}}} males.
So, for the third pick, with 9 males left out of 20 available students,
the probability of picking one male is {{{9/20}}} .
The probability that a female is selected, then two males is
{{{(12/22)*(10/21)*(9/20)=12*10*9/(22*21*20)=highlight(9/77)}}}
 
For the first pick, with 12 females out of 22 students,
the probability of picking one female is {{{12/22}}} .
After that, for the second pick, with 11 females out of 21 available students,
the probability of picking another female is {{{11/21}}} .
After that second pick, you are left with {{{22-2=20}}} students, including 10 males.
So, for the third pick, with 10 males left out of 20 available students,
the probability of picking one male is {{{10/20}}} .
Then, the probability that two females are selected first, then one male is
{{{(12/22)*(11/21)*(10/20)=12*11*10/(22*21*20)=highlight(1/7)}}} .
 
For the first pick, with 10 males out of 22 students,
the probability of picking one female is {{{10/22}}} .
After that, you are left with with 9 males out of 21 available students,
and then the probability of picking another male is {{{9/21}}} .
After that second pick, you are left with {{{22-2=20}}} students, including {{{10-2=8}}} males.
So, for the third pick, with 8 males left out of 20 available students,
the probability of picking one more male is {{{8/20}}} .
Then, the probability that three males are selected is
{{{(10/22)*(9/21)*(8/20)=10*9*8/(22*21*20)=highlight(6/77)}}} .
 
For the first pick, with 12 females out of 22 students,
the probability of picking one female is {{{12/22}}} .
After that, for the second pick, with {{{12-1=11}}} females out of {{{22-1=21}}} students,
the probability of picking another female is {{{11/21}}} .
After that second pick, you are left with {{{22-2=20}}} students, including {{{12-2=10}}} females.
So, for the third pick, with 10 females left out of 20 available students,
the probability of picking one more female is {{{10/20}}} .
So, the probability that three females are selected is
{{{(12/22)*(11/21)*(10/20)=12*11*10/(22*21*20)=highlight(1/7)}}}