Recent content by snaidu228

Homework Statement There are a total of 30 members of Parliament in a new country called JanesWorld. Among these deputies, there are 10 from the “Conservative Janes” , 8 from the “Progressive Janes” and 12 independents . How many ways can Queen Jane form a parliamentary committee of 11...

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Homework Statement 1) What is the coefficient of x^43 in the expansion of [(2/x^2) − x3)^16? (2) What is the coefficient of x^14y^12 in the expansion of (3x − 2y)^26? Homework Equations Binomial Expansion The Attempt at a Solution For (1), I started out like this: (16...

Homework Statement Prove that, in any set of n + 1 positive integers (n ≥ 1) chosen from the set {1, 2, . . . 2n}, it must be that two of them are relatively prime (i.e. have no common divisor except 1). ( Hint: two consecutive integers are relatively prime. Make boxes labelled by pairs of...

Homework Statement Prove that, in any set of n + 1 positive integers (n ≥ 1) chosen from the set {1, 2, . . . 2n}, it must be that two of them are relatively prime (i.e. have no common divisor except 1). ( Hint: two consecutive integers are relatively prime. Make boxes labelled by pairs of...

PigeonHole Help! Homework Statement A computer password is formed from 4, 5 or 6 characters. A character is either a lowercase or uppercase vowel: (a, e, i, o, u, y) or (A, E, I, O, U, Y) (passwords are case sensitive) or else it is a digit from the set {0, 3, 4, 7, 9}. Each password must...

Homework Statement Prove that every integer n>= 14 is a sum of 3's and/ or 8's. Homework Equations Induction Hypothesis The Attempt at a Solution Base Case: P(0): Suppose n= 14, and k is an integer representing number of times 3 or 8 is added: 14= 3k; k=14/3 ( this shows...

Homework Statement If x is a real number, we define [x] as being the largest integer <= x. For example, [1.2] = 1, [-1.1] = -2, [1] = 1, [11/3]3 = 3, . . . Let {an}n>=1 be the numerical sequence defined by: a1 = 3; and an = a[n/2], for n>=2 (a) Give the terms a1; a2; ... ; a8 of this...

Homework Statement I need a little help in understand this question: Let E and F be two sets, R a binary relation on the set E and S a binary relation on the set F. We define a binary relation, denoted RxS, on the set ExF in the following way ("coordinate- wise"): (a,b) (RxS) (c,d) <-->...