How many different ways could the funds be split up

Reference no: EM13995018

1. Consider the following

Claim. The number n(n + 1) is an odd number for every n.

Proof. Assume the statement is true for n. We prove the statement for n + 1 by induction. Note that

(n + 1)((n + 1) + 1) = n(n + 1) + 2(n + 1).

By induction n(n + 1) is odd. Thus, (n + 1)((n + 1) + 1) is the sum of an odd number n(n + 1) and an even number 2(n + 1). The sum of an odd number and an even number is odd. Thus, we have proved the claim by induction.

I checked the claim and it doesn't seem to work for n = 15, since 15.16 = 240, which is even. What is wrong with the proof?

2. Six poker players each start with $5. After an evening of play where all bets are multiples of $.10, how many different ways could the funds be split up?

3. Our class has 24 registered students. Each student will get an A, B, C, D, or F (we assume there are no Ws or Is).

(a) How many ways are there to assign the grades to the class (and no, you may not assume you get an A)?

(b) Suppose I need to report my grade distribution (how many As, how many Bs, etc) to my department; how many possible grade distributions are there for this class?

(c) Suppose that for every grade, there is at least one student who received that grade. How many grade distributions are there now?

4. For each of the following sets, count the number of 4 letter words that one can make using letters from the set.

(a) The set {A, B, C, D, E, F, tt, H, I} (ABCD is valid, but AABC is not).

(b) The multi-set {T, E, L, E, P, H, O, N, E} (EELE is valid, but EEEE is not).

5. In poker, the more likely a hand is to appear, the less valuable it is. For the following 5 card hands, determine their probability of appearing, and then order the hands by value:

(a) 5-card flush

(b) four of a kind

(d) 5-card straight

6. A 5 digit number contains no zeroes. What is the probability that it has exactly three distinct digits?

Reference no: EM13995018

Questions Cloud

Solve the tower of hanoi problem : Give the minimal number of steps to solve the Tower of Hanoi problem for d discs and 3 pegs - write in complete sentences.

What is the current at given time : Consider an L-R circuit as shown in the figure. The battery provides 12.0 V of voltage. What is the current I (t„) at a time after t=0 equal to three times the time constant?

Examine the three core conflicts : Reflect on which side of each conflict you may hold a preference as an emerging professional. Apply professional or personal experience and examine the three core conflicts. (You are not required to share personal or sensitive information.)

Find the diameter of the falling water column : Water emerges from a faucet of diameter 3cm in a steady, near vertical flow with speed 2.0 m/s. At the distance 10cm below the faucet, find the diameter of the falling water column.

How many different ways could the funds be split up : What is the probability that it has exactly three distinct digits and how many different ways could the funds be split up - determine probability of appearing, and then order the hands by value:

What is the gauge pressure at the exit : Water enters a horizontal pipe with a velocity of 3.0 m/s and exits with a velocity of 6.0 m/s. If the gauge pressure at the entrance is 55 kPa, what is the gauge pressure at the exit? Density of water is 1000 kg/m3.

Erikson theory and the commentary : Refer to and apply Erikson's theory and the commentary provided in this week's textbook readings on midlife crisis. Relate Erikson's work specifically to personal priority rearrangements that may occur in middle adulthood. Explain how the concept of ..

What personality traits do leaders like : What personality traits do leaders like Todd McFarlane possess that distinguish them from other individuals? How have global competition and technology advances changed business conditions and leadership challenges

Applicant receives a job interview : Ascertain the key factors an employer may take into consideration when determining whether or not an applicant receives a job interview.

User Account

All Pages