Suppose that 30 different computer games and 20 different toys are to be distributed among three different bags of Christmas presents. The first bag is to have 20 of the computer games. The second bag is to have 15 toys. The third bag is to have 15 presents, any mixture of games and toys. How many ways are there to distribute these 50 presents among the three bags?

465,817,912,560 ways

Step-by-step explanation:

This problem of selection is a combination problem

There are 30 different computer games and 20 different toys

The first bag is to contain 20 computer games, this means we're to select 20 computer games from 30 computer games. This can be done in

³⁰C₂₀ ways = 30,045,015 ways

The second bag is to have 15 toys, this means we're to select 15 toys from 20 toys. This can be done in

²⁰C₁₅ ways = 15,504 ways

Then the remaining toys and computer games are put into the last bag

¹⁵C₁₅ = 1 way

Total number of ways to distribute the toys and computer games among 3 bags = 30,045,015 * 15,504 * 1 = 465,817,912,560 ways