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I found this neat question on my test, anyone can solve it? Many solutions with different ways to solve is welcomed and needed.

In a bag there are $200$ marbles consisting of $60$ red marbles, $60$ blue marbles, $60$ green marbles, and the rest are $20$ white marbles and yellow (white and yellow in $1$ marbles). If the marble is chosen without looking, what is the minimum amount that must be taken in order from the selected minimum marbles consists of $20$ marbles of the same color?

  • A.) $58$
  • B.) $57$
  • C.) $68$
  • D.) $78$
  • E.) $79$

Please Show Your Work!

1 Answers 1

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The game is to get $20$ marbles with the same color, we pick them one by one and we stop as soon as we reach the $20$'s. There is a worst-case scenario-in terms of number of picks- that will lead to the win.

First, we are so unlucky that we pick all yellows and whites, that is $20$ taken.Worse, we pick $19$ reds, $19$ blues ,and $19$ greens. The next pick is a winning one as we will either have $20$ reds,blues or greens.

Therefore , the number of picks in the worst case scenario that leads to the win is $$20+19*3+1=78$$