DJ Giovanni is making a playlist for a friend; he is trying to decide what 12 songs to play and in what order they should be played. If he has his choices narrowed down to 22 country, 11 reggae, and 5 pop songs, and he wants to play an equal number of country, reggae, and pop songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.

5.78×10¹⁵

Step-by-step explanation:

The playlist has 12 songs, and he wants the same number of songs for each genre, so he must pick 4 songs per genre.

The number of ways he can choose 4 country songs (ignoring the order) is ₂₂C₄ = 7315.

The number of ways he can choose 4 reggae songs (ignoring the order) is ₁₁C₄ = 330.

The number of ways he can choose 4 pop songs (ignoring the order) is ₅C₄ = 5.

The total number of combinations is 7315 × 330 × 5 = 1.21×10⁷.

Once he has his 12 songs selected, the number of ways he can arrange them is ₁₂P₁₂ = 12! = 4.79×10⁸.

So the total number of possible playlists is:

(1.21×10⁷) × (4.79×10⁸) = 5.78×10¹⁵

what are the answear choices to the question.

step-by-step explanation:

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.