A box contains six red balls and four green balls. Four balls are selected at…
2018
A box contains six red balls and four green balls. Four balls are selected at random from the box. What is the probability that two of the selected balls will be red and two will be in green?
- A.
\(1 \over 14\) - B.
\(3 \over 7\) - C.
\(1 \over 35\) - D.
\(1 \over 9\)
Attempted by 23 students.
Show answer & explanation
Correct answer: B
Use combinations to count outcomes without regard to order.
Number of ways to choose 2 red balls from 6: C(6,2)=15
Number of ways to choose 2 green balls from 4: C(4,2)=6
Total favorable outcomes (2 red and 2 green): 15 × 6 = 90
Total ways to choose any 4 balls from 10: C(10,4)=210
Probability = favorable / total = 90/210 = 3/7
Final answer: 3/7