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There are n sweets in a bag. 6 of the sweets are orange. The rest of the sweets are yellow. Hannah takes a sweet from the bag and eats it. Hannah then takes at another sweet. The probability that Hannah eats two orange sweets is 1/3. Show that n²-n-90=0

P(2 orange sweets) = P(orange sweet) * P(orange sweet)

(6/n) * (5/(n-1)) = 1/3

30/(n(n-1)) = 1/3

90 = n(n-1)

90 = n2-n

n2-n-90=0 as required

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