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A box contains 5 green, 4 yellow and 3 white balls. Three balls are drawn at random. What is the probability that they are not of same colour.

A. $\frac{52}{55}$

B. $\frac{3}{55}$

C. $\frac{41}{44}$

D. $\frac{3}{44}$

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Correct Answer : C.

Total cases =

{}^{12}c_{3}

= \frac{12 \times 11 \times 10}{3 \times 2 \times 1} = 220

Total cases of drawing same colour =

{}^{5}c_{3} + {}^{4}c_{3} + {}^{3}c_{3}

\frac{5 \times 4}{2 \times 1} + 4 + 1 = 15

Probability of same colur

= = \frac{15}{220} = \frac{3}{44}

Probability of not same colur =

1 - \frac{3}{44}

=

\frac{41}{44}

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