Answer to Question #13079 in Combinatorics | Number Theory for Patti

Question

i have 40 equal squares in 4 columns and 10 rows. If I chose one square from each column, how many groups of 4 is possible ? I began counting but it got overwhelming so I need to know if there's a formula. The order of the group doesn't need to be consecutive in the sense that if the 4 squares on the first top row is 1.2.3.4 and the 2nd top row squares are 5,6,7,8. Then 1,2,3,8 or 2,8,1,3 is the same group..doesn't matter the order. As long as One is selected from each row, I imagine the amount of groups that is possible is over 10,000

Answer 1

First, you choose one square from 10 from the first row, then one from the second row and so on. Thus there are

N = 10^4 = 10000

possible ways to choose one square from each column, so there are 10000 possible groups of 4.