Combinatorics (original) (raw)

How many onto (or surjective) functions are there from an n-element (n >= 2) set to a 2-element set?

What is the possible number of reflexive relations on a set of 5 elements?

There are 100 students. 85 choose Math, 80 choose Physics, 75 choose Chemistry, 70 choose Biology. What is the minimum number of students choosing all 4 subjects? Assume each student chosen at least one subject.

A dice is thrown. Let A be the event that the number obtained is greater than 5. Let B be the event that the number obtained is less than 5. Then P (AUB) is

Let G be a group of order 6, and H be a subgroup of G such that 1<|H|<6. Which one of the following options is correct?

• Both G and H are always cyclic
• G may not be cyclic, but H is always cyclic
• G is always cyclic, but H may not be cyclic
• Both G and H may not be cyclic

There are 6 jobs with distinct difficulty levels, and 3 computers with distinct processing speeds. Each job is assigned to a computer such that:

• The fastest computer gets the toughest job and the slowest computer gets the easiest job.
• Every computer gets at least one job.

The number of ways in which this can be done is ___________.

The number of bit strings of length 8 that will either start with 1 or end with 00 is?

How many substrings of different length (non-zero) can be formed from a character string of length n ?

Two girls have picked 10 roses, 15 sunflowers and 14 daffodils. What is the number of ways they can divide the flowers amongst themselves?

Which one the following is a closed form expression for the generating function of the sequence {an}, where an = 2n + 3 for all n = 0, 1, 2,...?

There are 22 questions to complete.

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