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

 

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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?

 

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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

 

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

 

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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?

 

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

 

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

 

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

 

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

 

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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.

 

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