Suppose you have 150 video games for different video game consoles (43 Playstati

Question

Suppose you have 150 video games for different video game consoles (43 Playstation4 games, 29 XBOXOne games, and 78 Steam games.) Assume that all 150 video games are different. a) In how many ways can you put the 150 video games in a row on a shelf? b) In how many ways can you get a bunch of 10 video games to give to a friend? c) In how many ways can you get a bunch of twelve Steam Games and nineteen Xbox One Games to give to a friend? d) In how many ways can you put the 150 games in a row on a shelf if the Xbox One games are on the left, the Steam Games are in the middle and the Playstation4 are on the right?

Explanation / Answer

1) P - Playstation4 game = 43

X -Xboxone games = 29

S - Steam games = 78

a) all games are different

hence number of ways we can put the 150 video games in a row = 150 !

b) number of ways we can get a bunch of 10 games = 150 C 10 = (150 !)/(10 ! * 140!)

c)number of ways we can get 12 S and 19 X = 78 C 12 * 29 C 19

d) number of ways we can arrange 150 games where X on the left , S in middle and P on the right

= 43 ! * 29 ! * 78 !

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