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Help! Permutation and Combination question?
Mrs. Harper is randomly selecting 4 students to give their presentations today. If there are 16 boys and 14 girls in the class, what is the probability that the first two students selected are girls and the next two are boys.
Please explain how to get the answers
Thank You!
2 Answers
- M3Lv 78 years agoFavorite Answer
since the order is specified,
it is much simpler to compute probabilities directly
Pr = (14/30 *13/29) *(16/28 *15/27)
= 52/783, ≈ 0.0664
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- 8 years ago
There are (16C2) times (14C2) ways of choosing two boys and two girls, and for each choice, there are 2X2 ways of arranging them whilst still maintaining the correct order **. This gives (16C2)X(14C2)X4 possibilities.
The total number of ways of selecting 4 students out of 30, order being important, is (30C4)X4! (which incidentally = 30P4, where P denotes permutations)
So the probability = (16C2)X(14C2)X4 / (30C4)X4! =120X91X4/(30X29X28X27) = 0.0664
** To explain the 2X2 factor, suppose the girls and boys chosen were g1, g2, b1 and b2. Then we have the following 4 different possibilities for the same choice of students and the same order of presentation, namely two girls and then two boys:,
g1,g2,b1,b2
g2,g1,b1,b2
g1,g2,b2,b1, and
g2,g1,b2,b1
