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Discrete Math
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How many bit strings of length 10 either begin with three 0s or end with two 0s?
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A bank account is opened with a deposit of \$50,000. At the end of each year, the account earns:
- 10% interest on the current balance, and
- 5% of the previous year's balance as bonus.
No money is withdrawn. How much is in the account at the end of year 3?
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Find the solution to the recurrence relation:
with initial conditions
.Which of the following is the closed-form solution?
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Let . A partition of into subsets and is called if the sums of the elements in and are equal. Determine the number of special partitions of . !
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Solve the following recurrence relation: with initial condition . The answer is given in the form: . What is the value of ? (Enter answer)
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How many ways are there to distribute five indistinguishable objects into three indistinguishable boxes? (Enter answer)
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How many possible outcomes are there for a cooking contest with three chefs if ties are allowed? [Note: Two or three chefs may tie.] (Enter answer)
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What is the minimum number of students that must be enrolled in the promotion 2023 of USTH to guarantee that there are at least 30 students who were born in the same month (not necessarily the same year).
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There are 5 questions in the final exam. How many ways are there to assign points to the questions if the total number of points is 20 and the number of points for each question must be an integer not smaller than 2?
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In how many ways can a photographer at a wedding arrange 6 people, including the bride and the groom, in a row so that the bride is next to the groom.
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