Answer to Question #341557 in Statistics and Probability for mont

Question

If Johnny had 20 complete living room outfits, disregard color scheme, how many different sets of five complete outfits could be arranged?  

Answer 1

The number of possible sets is 

$$^{N}C_n=^{20}C_5=\dbinom{20}{5}=\dfrac{20!}{5!(20-5)!}$$

$$=\dfrac{20(19)(18)(17)(16)}{1(2)(3)(4)(5)}=15504$$