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- The '''ball-and-urn''' technique, also known as '''stars-and-bars''', '''sticks-and-sto If you could only put one ball in each urn, then there would be <math>{n \choose k}</math> possibilities;5 KB (795 words) - 16:39, 31 December 2024
- 65 bytes (10 words) - 18:05, 29 October 2024
Page text matches
- ...xes and <math>n>k</math>, then at least one box must contain more than one ball. ...math> boxes where <math>n>k</math> such that all boxes contain at most one ball.11 KB (1,986 words) - 18:13, 19 June 2024
- This is recommended to be learned around the time you are introduced to the [[Ball-and-urn]] method, so that you can become increasingly familiar with the mor1,016 bytes (141 words) - 02:39, 29 November 2021
- ...e the top of spherical ball with a radius of <math>8.</math> The spherical ball, lying atop a flat floor, casts a shadow. What is the area of this shadow?12 KB (1,784 words) - 15:49, 1 April 2021
- ..."balls" into <math>s</math> identical "boxes" with at most <math>1</math> ball per box, for <math>s=1</math> to <math>s=5</math>. This is equivalent to <m9 KB (1,409 words) - 02:59, 8 December 2024
- ...order doesn’t matter between different tail flips this just becomes the ball-and-urn argument. We want to add 5 balls into 4 urns, which is the same as4 KB (772 words) - 20:09, 7 May 2024
- ...all from her bag and puts it into Bob's bag. Bob then randomly selects one ball from his bag and puts it into Alice's bag. What is the probability that aft ...puts in Bob's bag doesn't matter. [[Without loss of generality]], let the ball Alice puts in Bob's bag be red.1 KB (211 words) - 03:32, 4 November 2022
- When a light beam reflects off a surface, the path is like that of a ball bouncing. Picture that, and also imagine X, Y, and Z coordinates for the cu3 KB (591 words) - 14:11, 21 August 2019
- ...all from her bag and puts it into Bob's bag. Bob then randomly selects one ball from his bag and puts it into Alice's bag. What is the probability that aft14 KB (2,059 words) - 00:17, 30 January 2024
- ...ll is coloured red or blue, and there is at least one of each colour. Each ball weighs either 1 pound or 2 pounds, and there is at least one of each weight4 KB (604 words) - 03:32, 8 October 2014
- ...categories, since it is assumed that their order is unimportant. Using the ball and urns/sticks and stones/stars and bars formula, the number of ways to do Also known as the [[ball-and-urn]] technique.7 KB (993 words) - 20:06, 29 September 2024
- ...shop class is making a golf trophy. He has to paint 300 dimples on a golf ball. If it takes him 2 seconds to paint one dimple, how many minutes will he ne13 KB (1,990 words) - 08:51, 19 June 2024
- ...shop class is making a golf trophy. He has to paint 300 dimples on a golf ball. If it takes him 2 seconds to paint one dimple, how many minutes will it ta655 bytes (96 words) - 12:33, 31 July 2024
- ...4</math>, and <math>\displaystyle 5</math>? (NOTE: After placing the last ball of a certain color in a box, you still place the balls of the other colors7 KB (1,110 words) - 04:15, 31 December 2006
- ......, 28 are deposited in bin B at step 7 of this process.) In which bin is ball 2024 deposited? ...> will be in row <math>64</math>. Since <math>64 \equiv 4 \bmod{5}</math>, ball <math>2024</math> will be placed in bucket <math>\boxed{\text{D. } D}</math2 KB (366 words) - 20:51, 21 December 2024
- ...e balls, <math>2</math> red balls, a brown ball, a white ball, and a black ball. These balls are randomly drawn out of the box one at a time (without repl6 KB (990 words) - 14:23, 11 November 2009
- ...git); then we wish to drop <math>7</math> balls into these urns. Using the ball-and-urn argument, having <math>9</math> urns is equivalent to <math>8</math950 bytes (137 words) - 09:16, 29 November 2019
- ...er the 3x3 that is next to the 3 boxes we have filled in. We must put one ball in each row (since there must be 2 balls in each row and we've already put ...umn with two balls already, we can choose any of the 3 boxes for the third ball. This forces the location for the last two balls. So we have <math>3 \cdo14 KB (2,337 words) - 08:37, 10 January 2025
- ...the balls. Then Jill reaches into the jar and randomly removes a different ball. The probability that the sum of the two numbers on the balls removed is ev4 KB (694 words) - 21:00, 12 January 2024
- ...les of past mini-events are the estimathon, geometry bee, science bowl (or ball), and Tetris.3 KB (484 words) - 19:04, 12 March 2024
- A soccer ball is an example of an icosahedron with the vertices flattened into pentagonal790 bytes (117 words) - 12:01, 25 August 2019