The number of ways to arrange 𝑛 people in a row is 𝑛! n!. For 5 people, this is 5!=5×4×3×2×1=120.
The number of ways to choose 𝑘 people from 𝑛 is given by 120
The number of ways to arrange the letters of a word with all distinct letters is 𝑛! For "AIME", which has 4 letters, the number of arrangements is 4!=4×3×2×1=24.
The number of ways to choose 2 cards from 52 is given by 1326
This is a problem of distributing indistinguishable objects (candies) into distinguishable bins (children) with the restriction that each bin gets at least one object.
This is solved using the stars and bars method. We first give each child one candy, then distribute the remaining 2 candies among the 3 children. The number of ways is given by 6.
