Each factor of 210 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 45? Pick one.
A) 1/16 B) 5/42 C) 1/8 D) 3/16 E) 1/4
210=2*3*5*7, so the # of factors 210 has is (1+1)(1+1)(1+1)(1+1)=16 (see below);   42=2*3*7, so out of 16 factors only two are multiples of 42: 42 and 210, itself;   So, the probability is 2/16=5/42.   Answer: 5/42.
<result>B</result>
Each factor of 210 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 45?