An urn contains 5 different red and 6 different green balls. In how many ways can 6 balls be selected so that there are at least two balls of each colour?

425

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245

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125

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625

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Solution

The correct option is A 425
Total number of red balls = 5
Total number of green balls = 6
Possbile combination are:
$\begin{matrix} R e d & G r e e n 2 & 4 3 & 3 4 & 2 \end{matrix}$
$R e q u i r e d n u m b e r o f s e l e c t i o n s = (^{5} C_{2} \times^{6} C_{4}) + (^{5} C_{3} \times^{6} C_{3}) + (^{5} C_{4} \times^{6} C_{2}) = 425$

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An urn contains 5 different red and 6 different green balls. In how many ways can 6 balls be selected so that there are at least two balls of each colour?

The correct option is A 425Total number of red balls = 5 Total number of green balls = 6 Possbile combination are: RedGreen243342 Required number of selections = (5C2×6C4) + (5C3×6C3) + (5C4×6C2) = 425