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A box contains $15$ blue balls and $45$ black balls. If $2$ balls are selected randomly, without replacement, the probability of an outcome in which the first selected is a blue ball and the second selected is a black ball, is _____

  1. $\frac{3}{16}$
  1. $\frac{45}{236}$
  1. $\frac{1}{4}$
  1. $\frac{3}{4}$
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It is given that from a box containing $15$ blue balls and $45$ black balls, $2$ balls are selected randomly without replacement.

Probability that, the first selected is a blue ball and the second selected is a black ball  

$\qquad = \dfrac{^{15}C_{1}}{60} \times \dfrac{^{45}C_{1}}{59}$

$\qquad = \dfrac{15}{60} \times \dfrac{45}{59} = \dfrac{45}{236}.$

So, the correct answer is $(B).$
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