A cricket umpire has to pick 6 caps and 4 sweaters before a match. She picks up 3 articles at random. Determine the probability that at least one sweater was picked by the umpire ?

We have to find the probability that the umpire picked up at least 1 sweater. 

It means that we can subtract the probability in which no sweater was picked (i.e. picking up 3 caps) from 1 to get the desired probability. 

Number of ways in which 3 caps were picked = $$\large{6_{\large{C_3}}}$$

Number of ways in which 3 articles were picked = $$\large{10_{\large{C_3}}}$$

Probability of picking up 3 articles with no sweaters = $$\dfrac{\large{6_{\large{C_3}}}}{\large{10_{\large{C_3}}}}$$ = $$\dfrac{1}{6}$$

Probability of picking up at least 1 sweater = $$1-\dfrac{1}{6}=\dfrac{5}{6}$$

Hence, the probability of an umpire picking up 3 articles with at least 1 sweater is $$\dfrac{5}{6}$$.

Option D.