Sophie is choosing an outfit for the day. She has a choice of four pairs of pants, three shirts, and four pairs of shoes. How many different outfit choices does she have? 28 34 40 48

I think that there is no limitation about the combination amongst pants, shirts and shoes. This means that there are 3 different kinds and 11 pieces of them. So, the potential combinations are: 3^11 = 177147 A number which declares that Sophie has more than 48 choices. But this is an extraordinary number of choices taking into account the limitation that anytime the choice includes one kind of each. So, taking advance of the minimum number of pieces kind the 3 shirts in which one shirt will be choose at least, and then there is the following combination: 3^4 + (3*4^4) = 768 outfit choices. 3^4 for shirts and punts 3 for shirts 4^4 for punts and shoes