In a race in which twelve automobiles are entered and there are no ties, in how many ways can the first three finishers come in?

1320 ways

Step-by-step explanation:

In a race in which twelve automobiles are entered and there are no ties.

We have to find the ways in which first three finishers come in.

In these questions when order is fixed means when first, second and third positions are fixed (First comes, then second and then third) then we use the permutation to find the number of ways.

3 positions out of 12 automobiles =

=

=

= 12×11×10

= 1320

In 1320 ways first three automobiles may come in.

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐