Counting Mathematics for Computing (IT1030) - Sequences
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Questions and Answers

What is a sequence?

  • A list of letters in a specific order
  • A list of numbers in a specific order (correct)
  • A list of numbers in any order
  • A list of numbers in random order

Which type of sequence has a common difference between successive terms?

  • Infinite sequence
  • Geometric sequence
  • Arithmetic sequence (correct)
  • Finite sequence

Which notation is used to represent the sum of a sequence?

  • Sigma notation (correct)
  • Permutation notation
  • Pi notation
  • Factorial notation

What does 'Pi notation' represent?

<p>Product of elements (A)</p> Signup and view all the answers

What is the factorial of 0?

<p>1 (B)</p> Signup and view all the answers

In counting theory, what does the 'sum rule' refer to?

<p>Counting the total number of ways that a task can occur (A)</p> Signup and view all the answers

What is a permutation?

<p>An arrangement of objects in a specific order (D)</p> Signup and view all the answers

What is the formula for the number of r permutations of a set of n elements?

<p>$nP_r = \frac{n!}{(n-r)!}$ (D)</p> Signup and view all the answers

When calculating combinations, what does the order of the arrangement signify?

<p>It is not important (B)</p> Signup and view all the answers

How many permutations can be made from a set of 5 distinct elements?

<p>$120$ (C)</p> Signup and view all the answers

What is the number of ways to choose 3 teams out of 16 teams for a competition?

<p>$\binom{16}{3}$ (C)</p> Signup and view all the answers

If there are 6 people and only 2 seats available, how many ways can they be seated?

<p>$6P2$ (C)</p> Signup and view all the answers

How many matches are played in total after the pool matches and before the final?

<p>10 (A)</p> Signup and view all the answers

After the pool matches, who will play against the second-placed team of Pool D?

<p>Winner of Pool C (A)</p> Signup and view all the answers

According to the sum rule, if there are 5 ways to do a task and 3 ways to do another task, how many ways are there to do both tasks?

<p>$5 + 3$ ways (D)</p> Signup and view all the answers

What is the total number of choices for a representative to a university committee if there are 37 members of the mathematics faculty and 83 mathematics majors?

<p>$37 \times 83$ choices (C)</p> Signup and view all the answers

In a sequence of two tasks, if the first task can be done in 4 ways and the second task in 5 ways, how many ways are there to perform the entire procedure?

<p>$4 \times 5$ ways (C)</p> Signup and view all the answers

Who would play against the second-placed team of Pool B after the pool matches?

<p>Winner of Pool A (A)</p> Signup and view all the answers

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