Johnny has 7 different colored marbles in his bag.  In how many ways can he choose three different marbles from his bag to play a game?
I need to count the number of combinations of 3 marbles out of 7, without regard to the order of the marbles. This is a classic combinatorics problem, and I can use the formula for combinations: n choose r, or nCr, which is n!/(r!(n-r)!), where n is the total number of items, r is the number of items chosen, and ! means factorial. Therefore, Johnny has 35 ways to choose three different marbles from his bag.

