Jimmy is going on a quick vacation, and is packing some clothes. He has twelve shirts, and wants to take three of them with him. How many ways can Jimmy choose his shirts?
These are the number of ways Jimmy can choose his shirts:
(123)=12!9!⋅3!=12⋅11⋅106=220
+2864 n!r!(n−r)! is the formula you always use in these types.
N represents number of items you are choosing out of, and r represents the number of items you are choosing.
+4 Well if he has 12 shirts, he has 12 to choose from. So 12 for the first choice, 11 for the second choice (because the first has been used), and 10 for the third choice. Thus, he has 12⋅11⋅10 choices, but they are counted 6 times each, so the answer is 220.
+220 For this problem, do this...
Use combinations for this problem. Substitute the combination formula to get 12!/9!*3!. Then simplify to get 12*11*10/6 which is 2*11*10 which equals 220.
Jimmy can choose his shirts in 220 ways.
~~Hypotenuisance
