A and B pick a card at random from a well shuffled pack of cards, one after the other replacing it every time till one of them gets a queen. If A begins the game, then the probability that A wins the game is

A ferris wheel has five cars, each containing four seats in a row. There are $20$ people ready for a ride. In how many ways can the ride begin? What if a certain two people want to sit in different cars?

An urn contains $6$ red, $4$ blue, $2$ green and $3$ yellow marbles. If four marbles are picked at random, what is the probability that at least one is blue?
$(a) \dfrac{5}{91}\quad(b) \dfrac{1}{35}\quad(c) \dfrac{1}{3}\quad(d) \dfrac{4}{105}\quad(e)$ None of these

In a certain code 'COMPUTER' is coded as 'LNBVQSFU'. How is 'BULKHEAD' written in that code?

A roller coaster has five cars, each containing four seats, two in front and two in back. There are $20$ people ready for a ride. In how many ways can the ride begin? What if a certain two people want to sit in different cars?

After $32$ years Raja will be $5$ times as old as he was $8$ years ago. How old is he today?

Ten distinct balls are put into nine indistinguishable boxes so that no box is empty. The number of ways of placing these balls is?

How to simplify this sequence?
$x^{-1}+2x^{-2}+3x^{-3}+\cdots$

Also find the values of $x$ for which the summation would converge.

Ans: $\dfrac{x}{(x-1)^2}$

In a throw of a dice, find the probability of getting an odd number?

There are $4$ boys and $4$ girls. They sit in a row randomly. What is the chance that all the girls do not sit together.