Circles and Pentagon

Number Theory Level pending

Two white circles and three black circles are placed at random in a pentagon shape, find the probability that the three black circles will be adjacent.

1 2 \large \frac{1}{2} 14 25 \large \frac{14}{25} 2 5 \large \frac{2}{5} 1 4 \large \frac{1}{4}

Ossama Ismail by Ossama Ismail , 63, Egypt

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1 solution

The arrangements are:

  1. B B B W W BBBWW

  2. B B W B W BBWBW

  3. B W W B B BWWBB

  4. B W B W B BWBWB

  5. B W B B W BWBBW

  6. B B W W B BBWWB

  7. W W B B B WWBBB

  8. W B W B B WBWBB

  9. W B B W B WBBWB

  10. W B B B W WBBBW

From the above, the arrangements that have 3 3 adjacent black circles are numbers 1,3,6,7 and 10.

The probability that 3 blackcircles are adjacent is 5 10 = \frac{5}{10}= 1 2 \frac{1}{2}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

There is a typo in the problem. "Three" must be "three"

A Former Brilliant Member - 4 years, 4 months ago

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Thanks. I've updated the problem statement to reflect this.

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Brilliant Mathematics Staff - 4 years, 4 months ago

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