nabayom
Hi all, for the below question can someone explain why using the permutation formula, 12C2 , to find the total number of ways Martha can draw 2 cards is incorrect. Thanks At an end-of-year party for the employees of a certain company, Martha has been given an opportunity to win as many as two prizes. She must draw, at random, exactly one numbered card from each of two boxes—each of which, in turn, contains exactly six cards, numbered from 1 to 6. If the sum of the two numbers is equal to 8, then Martha will win a tablet computer. And, if at least one of the two numbers is a 2, then Martha will win a smartphone.
12C2 means we’re choosing 2 items from a set of 12, without any conditions. But in Martha’s case, there’s a catch. She has to pick one card from each of the two boxes. So, while 12C2 would include scenarios like picking cards numbered 1 and 2 from the first box and none from the second, that’s not how Martha’s game works.
For this situation, the right approach with combinations would be 6C1×6C1.