# Thread: probability of picking A.P series.

1. ## 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?

2. ## Re: probability of picking A.P series.

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 ....

3. ## Re: probability of picking A.P series.

Hello, 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?

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?

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# out of 21 tickets marked

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