Question:
Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is :
Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is :
Show Hint
Count the 3-element subsets of {1,...,11} forming an A.P. by common difference d, and divide by C(11,3).
Updated On: Nov 5, 2026
- \(\frac{10}{99}\)
- \(\frac{5}{33}\)
- \(\frac{15}{101}\)
- \(\frac{5}{101}\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Total ways to select 3 numbers from 11: \(\binom{11}{3}=165\).
Take the numbers as \(1,2,\dots,11\). Three numbers \(a,\ a+d,\ a+2d\) with \(d>0\) require \(a+2d\le 11\).
Number of triples for each \(d\): \(d=1:9,\ d=2:7,\ d=3:5,\ d=4:3,\ d=5:1\).
Favourable = \(9+7+5+3+1=25\).
Probability = \(\dfrac{25}{165}=\dfrac{5}{33}\).
Answer: (2) \(\frac{5}{33}\)
Take the numbers as \(1,2,\dots,11\). Three numbers \(a,\ a+d,\ a+2d\) with \(d>0\) require \(a+2d\le 11\).
Number of triples for each \(d\): \(d=1:9,\ d=2:7,\ d=3:5,\ d=4:3,\ d=5:1\).
Favourable = \(9+7+5+3+1=25\).
Probability = \(\dfrac{25}{165}=\dfrac{5}{33}\).
Answer: (2) \(\frac{5}{33}\)
Was this answer helpful?
0
0
Top JEE Main Mathematics Questions
- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
- If , then the general value of is:
- The general solution of
- If the constant term in the binomial expansion of $\left(\frac{x^{\frac{3}{2}}}{2}-\frac{4}{x^l}\right)^9$ is $-84$ and the coefficient of $x^{-3 l}$ is $2^\alpha \beta$, where $\beta<0$ is an odd number, then $|\alpha l-\beta|$ is equal to_____
View More Questions
Top JEE Main Probability Questions
- Bag A contains 3 white, 7 red balls and bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from bag A, if the ball drawn is white, is:
- The probability that Ajay will not go to office is \(\frac{1}{5}\) and probability that Ajay and Vijay will not go to the office is \(\frac{2}{7}\), if their visits to office is independent of each other, then find the probability that Ajay will go to the office, but Vijay will not go, is
- Given set = {1, 2, 3, ..., 50} one number is selected randomly from the set. Find the probability that number is multiple of 4 or 6 or 7.
- A coin is biased so that a head is twice as likely as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is
- An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability that the first draw gives all white balls, and the second draw gives all black balls, is:
View More Questions
Top JEE Main Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
View More Questions