Question

Find the probability of each event. A class has five boys and nine girls. If the teacher randomly picks six students, what is the probability that he will pick exactly four girls?

Answer 1

Answer: $\dfrac{60}{143}$

Step-by-step explanation:

Given,  A class has five boys and nine girls.

Total students = 5+9=14

Number of ways to choose 6 students out of 14= $^{14}C_6$  [Using combinations]

Number of ways to choose 4 girls out of 6 (4 girls + 2 boys = 6 ) = $^{9}C_4\times\ ^{5}C_2$

If the teacher randomly picks six students, then the probability that he will pick exactly four girls:-

$\dfrac{^{9}C_4\times \ ^{5}C_2}{^{14}C_6}$

$=\dfrac{\dfrac{9!}{4!5!}\times\dfrac{5!}{2!3!}}{\dfrac{14!}{6!8!}}\\\\=\dfrac{1260}{3003}\\\\=\dfrac{60}{143}$

hence, the required probability = $\dfrac{60}{143}$ .