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1.) A group of 9 people is going to be formed into committees of 4,3, and 2 people. How many committees can be formed if no person can serve on more than one committee?
2.) In men's tennis tournament at wimbleton , two finalists, A and B, are competing for the title, which will be awarded to the first player to win three sets. in how many different ways can the match be completed?
3.) A state motor vehicle department requires learners to pass a written test on the motor vehicle law of the state. The exam consists of ten true-false questions, of which eight must be answered correctly to qualify for a permit. In how many different ways can a learner who answers all questions on the exam qualify for a permit?
A d-ary tree is a generalization of a binary tree in which each internal node has d children. Using Eytzinger"s method it is also possible to represent complete d-ary trees
A moving body is opposed by a force per unit mass of value cx and resistance per unit mass value of bv^2 where x and v are the displacement and velocity of the particle at t
A solution was prepared by mixing 4.00 ml 0.20 M NH3, 1.00 ml of 0.20 M HCl, and 5.00 ml of water. Calculate the concentration of NH3 and NH4+ in the final diluted solution.
Sarah is a moderately active woman. She weighs 130 pounds, is 68 inches tall, and is 25 years old. Based on the following formula, what are her caloric needs? What happens t
Yaya invests her savings in two accounts, one paying 4% interest per year and the other paying 10%. She has four times as much invested in the 4% account as in the 10% accou
Now consider a large yam. Your mad scientist laboratory has a laser-cutter chamber in which you can mount the yam; the lasers are able to rotate around it so that cuts can b
Consider the recurrence T(n)=3T(n - 1) + 1 with the initial condition that T(0) = 2. We know that we could write the solution down from Theorem 4.1. Instead of using the the
Suppose that V is a complex (i.e. F = C) inner-product space. Prove that if N, an element of L(V), is normal and nilpotent, then N = 0.
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