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Counting Mathematics for Computing (IT1030) - Sequences

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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?

Product of elements Signup and view all the answers

What is the factorial of 0?

1 Signup and view all the answers

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

Counting the total number of ways that a task can occur Signup and view all the answers

What is a permutation?

An arrangement of objects in a specific order Signup and view all the answers

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

$nP_r = \frac{n!}{(n-r)!}$ Signup and view all the answers

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

It is not important Signup and view all the answers

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

$120$ Signup and view all the answers

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

$\binom{16}{3}$ Signup and view all the answers

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

$6P2$ Signup and view all the answers

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

10 Signup and view all the answers

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

Winner of Pool C 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?

$5 + 3$ ways 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?

$37 \times 83$ choices 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?

$4 \times 5$ ways Signup and view all the answers

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

Winner of Pool A Signup and view all the answers