A child is putting white clothes on two dolls. There are three shirts with different shapes, and three pants with different shapes. The shirts and pants that one doll wore should not be put on to the other doll. After putting clothes to two dolls, she colors the shirts and pants with either gray or blue. The colors of the shirts and pants on each doll should be different. How many different possible outcomes are possible?
My work: (3 shirt choices for doll 1) x (Two colors available for that shirt for doll 1) x (3 pant choices for doll 1) x (Two colors available for the selected pants for doll 1) x (Two shirt choices available for doll 2) x (Only one color available for that shirt for doll 2) x (Two pants choices available for doll 2) x (Only one color available for the selected pants for doll 2)
so final result is 3 x 2 x 3 x 2 x 2 x 1 x 2 x 1 = 144 outcomes
But other answers I see give 72 outcomes
I am right? If not, Where have I gone wrong? Also can someone show me how to do this with P(n,r) rather then with my logic? Thank You