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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 green?

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UGC NET Computer Science (Paper 2) Dec 2018 Paper
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Answer (Detailed Solution Below)

Option 4 : 3/7
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Detailed Solution

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Data:

red balls = 6  

green balls = 4

To Find:  The probability that two of the selected balls will be red and two will be green

Calculation:

Total balls = 6 + 4 = 10

4 balls from 10 balls can be selected in 10C4

2 red balls can be selected in 6C2 ways.

2 green balls from 4 green balls can be selected in 4C2 ways.

Probability that two selected balls will be red and two will be green = \(\frac{{^6{{\rm{C}}_2}{ \times ^4}{{\rm{C}}_2}}}{{^{10}{{\rm{C}}_4}}} = \;\frac{{15 \times 6}}{{210}} = \;\frac{3}{7}\) 

Important Point

Since red and green ball is asked, we have multiplied
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