<p>Following is a math prob I could guess correctly but couldn't solve. Can anyone show me how to solve this kind prob? </p>
<p>The integers 1 through 6 appear on the faces of a cube, one on each face. If 3 such cubes are rolled, what' the probability that the sum of the numbers on the top faces is 17 or 18?</p>
<p>A. 1/108
B. 1/54
C. 1/27
D. 1/18
E. 1/16</p>
<p>Thanks in advance :)</p>
<p>The answer is 1/54.</p>
<p>You can have a total of 6x6x6 = 216 possibilities when the cube is rolled three times. But, how many different possibilities will give you the sum of 17 or 18?
Well, for 18, you have only one possibility which is 6 + 6 + 6.
And, for 17, you have three possibilities which are 5+6+6 or 6+5+6 or 6+6+5</p>
<p>So we have four possibilities that will give us the sum of 17 or 18.
4/216 = 1/54</p>
<p>Oh I thought there were only two possibilities to get a sum of 17 or 18 which were 6+6+6 and 5+6+6. I didn’t think I could get 6+5+6 or 6+6+5. It’s a permutation, right? where order doesn’t matter? I always mix up permutation and combination. </p>
<p>Thanks so much :)</p>
<p>Yes, it’s okay to have the same value in different order. Good luck.</p>