### Instruction: 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?### Response: 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.
In this case, n is 7, and r is 3, so I plug those into the formula and simplify: 7C3 = 7!/(3!(7-3)!) = (7*6*5*4*3*2*1)/(3*2*1*4*3*2*1) = (7*6*5)/(3*2*1) = 35.