Question

Counting a) You are buying 11 songs and there are 7 different genres to choose from. How many ways can you choose the 11 songs if you can have as many of each genre as you would like? b) How many solutions are there to the equation $x_1 + x_2 + x_3 + x_4 = 13$ where $x_1, x_2, x_3, x_4$ are nonnegative integers?

          Counting
a) You are buying 11 songs and there are 7 different genres to choose from. How many ways can you choose the 11 songs if you can have as many of each genre as you would like?
b) How many solutions are there to the equation $x_1 + x_2 + x_3 + x_4 = 13$ where $x_1, x_2, x_3, x_4$ are nonnegative integers?

Counting
a) You are buying 11 songs and there are 7 different genres to choose from. How many ways can you choose the 11 songs if you can have as many of each genre as you would like?
b) How many solutions are there to the equation x1 + x2 + x3 + x4 = 13 where x1, x2, x3, x4 are nonnegative integers?

Added by Adam M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Keerti J

Step 1

We have 11 songs to choose and 7 genres to choose from. We can think of this problem as distributing 11 identical stars among 7 different boxes (genres) with no restrictions on the number of stars in each box. Using the stars and bars formula, the number of ways Show more…

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15 Counting ) You are buying 11 songs and there are 7 different genres to choose from. How many ways can you choose the 11 songs if you can have as many of each genre as you would like? b)How many solutions are there to the equation 1 +2+3+4=13 where 1,2,314 are nonnegative integers?