Combinatorics | Number Theory Answers

Six professor begin courses on Monday, Tuesday, Wednesday, Thursday, friday, and Saturday, and announce their intention of lecturing at interval of 3,2,5,6,1and 4 days respectively the regulations of the university forbid Sunday a lecture(so that a Sunday a lecture must be omitted) when first will all six professors find themselves compelled to omit a lecture

Suppose f : N → N is a function defined by ƒ(x) = a(x + b), where a, b E N. If f is a bijective function,

then find the value of a + b.

Suppose f : N → N is a function defined by ƒ(x) = a(x + b), where a, b E N. If f is a bijective function,

then find the value of a + b.

Let us define a function f : N → Q as follows,

(n-1)/4 n is odd

f(n) = {

(n+1)/2 n is even

Which of the following are true?

f is not one to one.

f is not onto.

f is onto.

f is one to one.

In a Zoo, there are 6 Bengal white tigers and 7 Bengal royal tigers. Out of these tigers, 5 are males and 10 are either Bengal royal tigers or males. Find the number of female Bengal white tigers in the Zoo.

How many ways are there to arrange the letters in the word ALGORITHMS? Note, the letter arrangement does not have to spell a word in the dictionary, but the new word must contain all the letters and each letter can be used only once.

Hint: Start with shorter words (e.g ALG or ALGO) and see if a pattern emerges with the number of possible arrangements.

1. How many 4 digits numbers can we create from 3,4,5,6,7,0,9 if;
2. We need all numbers to be even numbers        [2]
3. We need all of them to be odd numbers        [2]
4. We need all of them to be divisible by 5        [3]
5. In how many different ways can we choose a committee that is comprised of two men and one woman from a group of 5 men and 4 women if;
6. We need a chosen committee member is selected only once (i.e. if a person occupies only one position in the committee)                [2]
7. We need to choose a chairperson, a treasurer and secretary [3]

In how many ways can we arrange the letters of the word EXCELLENT to form different 9 letter words, with or without meaning   

Determine whether -104 is a quadratic residue or non residue of the prime 997.

Suppose p=0.9 and n=4 ,C={0000,1010,1100}.Compute pC,v where

v=1100