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 

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

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