What is the total combination I will have if I have 13 children and each kid has a choice to choose one of these 3 fruits a pears, grapes and orange(of which i have unlimited supply of each fruit)........what is the total the number different of combinations i can get
Please see the 3 different pictures(charts) i have added to display each child picking a fruit . i have uploaded three different examples which are 3 different combinations,in which 13 children can choose one of three fruit
but i have sent you three different combinations but i want to know what is the total amount of combinations i can have enter image description here
Let refer to the Rule of product, we have 3 choices for each kid thus the number of combinations is
$$3\cdot 3\cdot...\cdot 3= 3^{13}$$
and more in general for $k$ kids and $n$ fruits the number of combinations is
$$n^k$$