Out of 21 tickets marked with numbers from 1 to 21, three are

drawn at random. Find the probability that the numbers on them are in Arithmetic Progression?

I can understand that there are C(21,3) outcomes.But how many A.P series can be there?

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- Dec 6th 2011, 07:35 PMearthboyprobability of picking A.P series.
Out of 21 tickets marked with numbers from 1 to 21, three are

drawn at random. Find the probability that the numbers on them are in Arithmetic Progression?

I can understand that there are C(21,3) outcomes.But how many A.P series can be there? - Dec 7th 2011, 02:21 AMmr fantasticRe: probability of picking A.P series.
- Dec 7th 2011, 08:00 AMSorobanRe: probability of picking A.P series.
Hello, earthboy!

Quote:

Out of 21 tickets marked with numbers from 1 to 21, three are drawn at random.

Find the probability that the numbers on them are in Arithmetic Progression

I can understand that there are C(21,3) outcomes.

But how many A.P series can be there?

There is no formula for your question.

I see no choice but to List them and Count them . . . and look for a pattern.

Sequences beginning with 1: .$\displaystyle \begin{Bmatrix}1,2,3 \\ 1,3,5 \\ 1,4,7 \\ 1,5,9 \\ \vdots \\ 1,10,19 \\ 1,11,21 \end{Bmatrix}$

Sequences beginning with 2: .$\displaystyle \begin{Bmatrix}2,3,4 \\ 2,4,6 \\ 2,5,8 \\ 2,6,10 \\ \vdots \\ 2,11,20 \end{Bmatrix}$

Sequences beginning with 3: .$\displaystyle \begin{Bmatrix}3,4,5 \\ 3,5,7 \\ 3,6,9 \\ 3,7,11 \\ \vdots \\ 3,12,21 \end{Bmatrix}$

. . . . . . . . . . . . . . . . . . . . . . . . . .$\displaystyle \vdots$

Sequences beginning with 17:.$\displaystyle \begin{Bmatrix}17,18,19 \\ 17,19,21\end{Bmatrix}$

Sequences beginning with 18:.$\displaystyle \begin{Bmatrix}18,19,20\end{Bmatrix}$

Sequences beginning with 19:.$\displaystyle \begin{Bmatrix}19,20,21\end{Bmatrix}$

Do you see a pattern?