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Probability Level 5

Dipa has $ 9 \$9 . Each day he buys either tea for $ 1 \$1 or orange juice for $ 2 \$2 or apple juice for $ 2 \$2 or avocado juice for $ 2 \$2 . In how many ways can he spend $ 9 \$9 ?


The answer is 1159.

Aira Thalca by Aira Thalca , 24, Indonesia

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1 solution

Alan Yan
Jan 14, 2018

Let S n S_n be the number of ways to spend n n dollars. Then S n = S n − 1 + 3 S n − 2 . S_n = S_{n-1} + 3S_{n-2}. Given the initial conditions S 1 = 1 , S 2 = 4 S_1 = 1, S_2 = 4 , we can compute S 9 = 1159 S_9 = 1159 .

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