A coordinator will select 6 songs from a list of 12 songs to compose an event's musical entertainment lineup. How many different lineups are possible

There are 924 different possible line ups

Step-by-step explanation:

Here, we want to find the number of different line ups possible

That can be found by using the combination system

Mathematically, in this case, that will be 12 C 6

= 12!/6!6! = 924

homozygous. one is homozygous, while two is heterozygous.

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)