Question

Dina's collection of 9 albums includes one country album, how many of these sets will not include the country album

Answer 1

Dina, choosing 4 albums from 10 (1 country), has 210 sets. 126 sets exclude the country album; 84 include it. The total choices offer various combinations for her road trip playlist.

a) To find the total number of different sets of four albums Dina can choose from her collection of ten albums (including one country album), we'll use the combination formula:

`\(\binom{n}{r} = (n!)/(r!(n - r)!)\)`

where
`\(n\)` is the total number of items to choose from and
`\(r\)` is the number of items to choose. In this case,
`\(n = 10\)` (total albums) and
`\(r = 4\)`

`\(\binom{10}{4} = (10!)/(4!(10 - 4)!) = (10 * 9 * 8 * 7)/(4 * 3 * 2 * 1) = 210\)`

Therefore, Dina can choose from 210 different sets of four albums.

b) To determine the number of sets that would not include the country album, we'll calculate the number of ways she can choose 4 albums out of the 9 non-country albums.

`\(\binom{9}{4} = (9!)/(4!(9 - 4)!) = (9 * 8 * 7 * 6)/(4 * 3 * 2 * 1) = 126\)`

Thus, there are 126 different sets of albums that would not include the country album.

c) To find the number of sets that would include the country album, subtract the number of sets without the country album from the total number of sets:

Total sets - Sets without country album = Sets with country album

(210 - 126 = 84)

Therefore, there are 84 different sets of albums that would include the country album.

complete the question

Dina's collection of ten albums includes one country album. Dina will choose four of her albums to play on a road trip. (Assume order is not important.)

a) How many different sets of four albums could she choose?

b) How many of these sets would not include the country album?

c) How many of them would include the country album?

a) Dina can choose from

b) There are

c) There are different sets of albums. sets that would not include the country album. sets that would include the country album.