My Math Forum What's the probability of getting one 3 when you roll a dice 4 times?

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 January 26th, 2015, 03:37 PM #1 Senior Member     Joined: Feb 2014 From: Louisiana Posts: 156 Thanks: 6 Math Focus: algebra and the calculus What's the probability of getting one 3 when you roll a dice 4 times? I know that the sample space consists of $\displaystyle 1296$ possible outcomes; however, I am not sure how to calculate the number of successes, that is, the value of the numerator. How would you do so using combinations $\displaystyle \binom{n}{k}$?
 January 26th, 2015, 03:58 PM #2 Member   Joined: Jan 2015 From: Orlando, Florida Posts: 92 Thanks: 10 when you say one 3 you mean exactly one 3 right? if this is the case, there are 4C1 ways to choose which die you roll the 3 on and 5^3 for what values the other dice obtain. 4x5^3/6^4=125/324

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