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?
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?
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?