1. Let us assume that we are allowed to print so called Mercy Money used for sho
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Question
1. Let us assume that we are allowed to print so called Mercy Money used for shopping only within Mercy College campus. The money is composed a unique serial numbers like M20130BC. It always start with M, follows with five digital numbers chosen from 0 to 9, and then two letters chosen from A to Z.
a. What is the total number of such series numbers?
b. What is the probability to getting the serial number M88888MM?
c. What is the probability of getting a serial number whose last two letters to be AA
2. College has several sports%u2019 teams. After surveying two teams, the student in math244 found that that there are 20 students in team A while 35 in team B. There are 6 in both teams (overlap).
a. How many team members in total in these two teams?
b. (bonus 5 points) The student then survey three teams. The results show that team A has 20, team B has 35, team C has 30. The overlap of team A and B is 6, team A and C is 5 and team B and C is 7. The overlap for all three teams (these members are in all three teams) is 3. What is the total numbers in all these three teams?
3. Is it possible to draw a general graph with degree sequence (4; 4; 2; 2; 3)? Explain
4. Prove that if we take 6 numbers from 1,2,3,%u2026 10, amongst the numbers selected are two whose difference is 5.
b.1. Prove the set 3Z^+ {3,6,9,12,15} is countable.
Explanation / Answer
1)
a) no of such series are = 1 * 10 * 10 * 10 * 10 * 10 * 26 * 26 = 67600000
b) probability fo getting serial number = 1/67600000
c) no of series of type M*****AA = 1 * 10*10 * 10 * 10 * 10 = 10^5
probability of getting a serial number with last two be AA = 10^5/67600000 = 1/676
2)
a) AUB = A + B - A int B
total no of memeners in both the teams = 20 + 35 - 6 = 49
b) total no of members inall these teams = 20 + 35 +30 - 6 -5 - 7 +3 = 70
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