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An urn contains $5$ boxes. Each box contains $5$ balls of different colors red, yellow, white, blue and black. Rangeela wants to pick $5$ balls of different colors ,a different colored ball from each box .If from the first box in the first draw, he has drawn a red ball and from the second box he has drawn a black ball , find the maximum number of trials that are needed to be made by Rangeela to accomplish his task if a ball picked is not replaced .

$\color{green}{a.)\ 12 }\\ b.)\ 11 \\ c.)\ 20 \\ d.)\ 60 \\ $

As the Ball need to be last place I though I would be $5+5+5=15$

But it is not given in options so I am confused.

I look for a short and simple way.

I have studied maths upto $12$th grade.

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The answer is 3+4+5 = 12

Two balls have already been found. When picking the third one, we just need any NEW color. Worst case scenario is we pick red and black, before picking a new color. So that's 3. The next one, worst case is picking all the previous 3 colors before finding a new color. So 4 balls are picked. Finally, worst case scenario for the last one is we pick every one we already have, 4, then the last one needed. So 5. 3+4+5=12

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    $\begingroup$ I agree with Jay! $\endgroup$ Commented Sep 6, 2015 at 7:18

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