# probability of picking A.P series.

• Dec 6th 2011, 07:35 PM
earthboy
probability 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 AM
mr fantastic
Re: probability of picking A.P series.
Quote:

Originally Posted by earthboy
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?

Think about how many arithmetic progressions are possible ....
• Dec 7th 2011, 08:00 AM
Soroban
Re: 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: . $\begin{Bmatrix}1,2,3 \\ 1,3,5 \\ 1,4,7 \\ 1,5,9 \\ \vdots \\ 1,10,19 \\ 1,11,21 \end{Bmatrix}$

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

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

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

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

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

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

Do you see a pattern?