DJ Howard is making a playlist for a radio show; he is trying to decide what songs to play and in what order they should be played.
If he has his choices narrowed down to reggae, pop, and rock songs, and he wants to play an equal number of reggae, pop, and rock songs, how many different playlists are possible?

The number of different playlists possible with order important = 1.9996 × 10¹³ ways = 2.00 × 10¹³ ways

Step-by-step explanation:

Selection problems in which the order matters are permutation problems.

So, the choices are 4 reggae songs from 11

4 pop songs from 12

4 rock songs from 23

number of ways = ¹¹P₄ × ¹²P₄ × ²³P₄ = 7920 × 11880 × 212520 = 19,995,921,792,000 = 1.9996 × 10¹³ ways

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

q1 a person or thing situated away or detached from the main body or system. a cluster is a a mash of many things.

q2 do

step-by-step explanation: