Sagar Chand

 7 If 4 people are seated randomly in a row of 8 seats, what is the probability that no 2 persons will sit on adjacent seats? 5 $6$ digit numbers formed from the first six positive integers such that they are divisible by both $4$ and $3$. 5 Inequality question: If $a + b + c =1$, what is the minimum value of $\frac{1}{ab} + \frac{1}{bc} + \frac{1}{ca}$. 5 How to do $\int e^\frac{-1}{2x^2}x^{-5}dx$? 3 How to calculate $a,b,c,d$ given the eigenvectors

### Reputation (1,612)

 +120 Number of cards to be pulled +110 Expected number of cards in original position in a shuffled deck of $52$ cards? +10 Random walk over a cube:Probability of returning back +10 What is the maximum length of sequence where the sum of 5 consecutive numbers in positive and sum of 8 consecutive numbers is negatve.

### Questions (8)

 12 Number of cards to be pulled 11 Expected number of cards in original position in a shuffled deck of $52$ cards? 10 Random walk over a cube:Probability of returning back 4 Expected number of turns for getting six 1's in six dice. 2 Can there exists a 6 digit number whose pairwise sum of digits is unique?

### Tags (69)

 16 combinatorics × 10 8 integration × 4 12 calculus × 6 8 combinations × 3 11 limits × 8 7 elementary-number-theory × 2 10 permutations × 7 6 probability × 9 9 inequality × 4 5 multivariable-calculus × 3

### Bookmarks (18)

 159 Taking Seats on a Plane 92 I roll a die repeatedly until I get 6, and then count the number of 3s I got. What's my expected number of 3s? 82 Expected Number of Coin Tosses to Get Five Consecutive Heads 54 Choose a random number between $0$ and $1$ and record its value. Keep doing it until the sum of the numbers exceeds $1$. How many tries do we need? 47 If a 1 meter rope is cut at two uniformly randomly chosen points, what is the average length of the smallest piece?