SOLUTION: Can I please have some help with process? There are 14 freshmen and 7 sophomores in a class. If three students are selected at random, find the probability that two are freshmen

Question 473914: Can I please have some help with process?
There are 14 freshmen and 7 sophomores in a class. If three students are selected at random, find the probability that two are freshmen and one is a sophomore. (to three decimal places.)
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
There are 14 freshmen and 7 sophomores in a class. If three students are selected at random, find the probability that two are freshmen and one is a sophomore. (to three decimal places.)
Solution:-
Solution:-
Freshmen 2
Sophomore 1
Total 3
Now
Using nCr=n! /(n-r)! r!
3 students can be chosen out of 21 = 21C3 ways.
= 21!/(21-3)!3!
= 21!/ 18!3!
=(21*20*19*18!) / (18! * 3*2*1)
= (21*20*19) /(3*2*1)
= 7980/6
= 1330 ways
1 Sophomore can be chosen out of 7 = 7C1
= 7! /(7-1)!1!
=7*6!/6!1!
= 7 ways
2 Freshmen can be chosen out of 14 = 14C2
=14!/(14-2)!2!
=14!/12!2!
=14*13*12!/12!2!
=14*13/2
=182/2
=91 ways
P(1 Sophomore & 2 Freshmen) = (7C1 * 14C2) / 21C3
= (7*91) /1330
=637/1330
=0.4789

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