tmua.me Extreme Set C Paper 1 · Question 19

Five cards are drawn successively without replacement from nine cards numbered $1,2,\ldots,9$ . Each remaining card is equally likely at each draw. The numbers, in order, are $y_0,y_1,y_2,y_3,y_4$ .

It is given that there exists a polynomial $f$ of degree at most $2$ such that

f(k)=y_k\qquad(k=0,1,2,3,4).

What is the probability that $f$ has degree exactly $2$ ?

\dfrac1{1890}

\dfrac17

\dfrac14

\dfrac12

\dfrac35

\dfrac25

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tmua.me Extreme Set C Paper 1 · Q19