3.55. a) How many three-digit numbers with different digits are there formed by digits belonging to the set ${4,5,6,7,8,9}$ and at the same time greater than $666 ?

Q: 1. How many three digit numbers can be formed from the digits 1,2,3,4 and 5 if one is not to used as…

A:

Q: Ex: An experimenter partitions a field into 64 same lots. Experimenter uses 5 different seeds, 3…

A: Given, No of Lots = 64 no of seeds = 5 no of pesticides = 3  no of fertilizers = 4

Q: 7. In how many ways can seven men and six women be arranged in a row so that the women occupy the…

A: Given, In an arrangement,Total men=7Total women=6 To find: Total ways of arrangement so that women…

Q: 8. The number of permutations of 11 objects taken 4 at a time is ---

A: Solution :  we have to find number of permutations of 11 objects taken 4 at a time.

Q: 17. The number of 3-digit numbers less than 500 that can be created if the last digit is either 4 or…

A: We have to form 3 digit numbers less than 500 with last digit is either 4 or 5

Q: 16. How many 6-element subsets of A = {0,1,2,3,4,5,6,7,8,9} have exactly three even

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Q: 5. How many 2-permutations are there of a set of eight objects?

A: We know that,  The formula pf permutations is,  nPr = P(n, r) = n!/(n-r)!

Q: 8. Suppose Jack has 1 red ball, 1 orange ball, 1 blue ball, 1 yellow 1, 1 black ball and 1 green…

A: Given :  jack has 1red ,1 blue,1 orange,1 yellow,1 black and 1 green ball then no of arrangement to…

Q: 2.How many license plates consisting of 6 digits (0 to 9) have their digits in nondecreasing order?

A: The numbers can start with 1, 2, 3, 4 or 5. As if it starts with any other number, it won’t be able…

Q: Show that if 5000 boys registered for driving license during the last month(31 days) at driving…

A: Given that 5000 boys registered for driving license during the last month in 31 days at driving…

Q: Suppose a set of 8 numbers are selected from the set: {1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}…

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Q: How many numbers must be selected from the set {2,4,6,8,10,12,14,16,18,20} to guarantee that at…

A: Use the principle of inclusion and exclusion to solve this problem, as in next step.

Q: Suppose 1/7 of the employees of certain companies work in the SOutheastern region. If the company…

A: Given that, 1/7 of the employees of certain companies work in the Southeastern region. Number of…

Q: How many numbers must be selected from the set {1, 2, 3, 4, 5, 6} to guarantee that at least one…

A: To find  How many numbers must be selected from the set {1, 2, 3, 4, 5, 6} toguarantee that at least…

Q: What is the size of the power set of S={1,2,3,4}?

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Q: 8. Show that the set (0, 1) – {1/2, 1/3, 1/4, -..} is uncountable.

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Q: Show that if seven integers are selected from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, there must be…

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Q: 8. Suppose Jack has 1 red ball, 1 orange ball, 1 blue ball, 1 yellow ball, 1 black ball and 1 green…

A: Given that  Jack has  Red ball = 1 Orange ball = 1 Blue ball  = 1 yellow ball = 1 black ball = 1…

Q: How many unordered sets are there of two items chosen from four? sets

A: To Find: How many unordered sets are there of two items chosen from four? Concept: Crn=n!r!n-r!

Q: 2.24 Students at a private liberal arts college are clas- sified as being freshmen, sophomores,…

A: Given: Students are classified as freshmen, sophomores, juniors and seniors. Hence, number of…

Q: Balls are numbered 1 through 10 (including 1 and 10) in an urn. 3 are drawn simultaneously and at…

A:

Q: How many subsets does the set  L = {3, 4, 5, 6} have?

A: Given, L = {3, 4, 5, 6}  No of elements in set L (n) = 4

Q: In how many ways can 16 balls be drawn from an urn containing 3 red balls, 8 white balls, and 5 blue…

A: We have given that,  Red balls = 3  White balls= 8  Blue  balls= 5 Then,  We wil find the how many…

Q: From the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, if five-digit numbers are to be formed and…

A: As per our guidelines we are supposed to answer only 3 sub-parts of any one question We have given…

Q: 1. Show that for n, mEZ", mEZ*, ged (2^-1,2m-)= 2 ged(n, m)_I

A: Suppose, in general, if p=gcdn,m then p=nx+my for some integers x, y Now if d=gcd2n-1,2m-1 then…

Q: Ex: Problem: Among a set of 5 black balls and 3 red balls, how many selections of 5 balls can be…

A:

Q: { n ∣ n ∈ N and 405 < n ≤ 437} H has --------  subsets. H has--------  proper subse

A: It is given that ,  H=n|n ∈N and 405 &lt; n ≤437we have to find , H has ................. subsets.H…

Q: How many three​-digit numbers may be formed using elements from the set​{1, 2, 3, 4, 5, 6, 7, 8, 9​}…

A: given:  set ​{1, 2, 3, 4, 5, 6, 7, 8, 9​}   if no element may be used more than once in a number and…

Q: Suppose that there are 27 students in discrete mathematics class. Show that the class must have at…

A: Here we solve this question by contradiction.

Q: How many unordered sets are there of two items chosen from eight?

A: To find unordered sets of two items chosen from eight. Number of unordered sets r chosen from n is…

Q: 2. Show that the combination of choosing r items from a set of n items has the same possible…

A: Combination can be defined as the number of ways of merging things disregarding of their orders.  It…

Q: A1. How many integers, greater than or equal to10000 but less than or equal to 39999, can be formed…

A: Since you've asked multiple parts questions, as per our answering guidelines we are supposed to…

Q: How many unordered sets are there of five items chosen from eight?

A: In unordered sets, the order of the selection of the selection of items does not matter. So,…

Q: How many unordered sets are there of four items chosen from six? sets

A:

Q: Suppose that 33% of McMaster undergraduate students are in their first year. President David Farrar…

A: It is given that p=0.33.

Q: How many three-digit numbers with different digits are there, formed from digits belonging to the…

A: The given digits are : 1,2,3,4,5,6,7,8,9 The total no. of digits given = 9 We are required to form a…

Q: How many subsets are there of the set N = {1, 44, 65, 11, 39, 53, 26}?

A: Given,          The set is N=1, 44, 65, 11, 39, 53, 26We know that,          The number of subsets…

Q: In how many ways can you partition a set of 8 elements into 3 subsets (compute S8.3)?

A: To find - In how many ways can you partition a set of 8 elements into 3 subsets compute S8, 3 ?…

Q: 5. Show that if there are 30 students in a class, then at least two have last name begin with the…

A:

Q: How many numbers lying between 100 and 1000 can be formed with the digits 0, 1, 2, 3, 4, 5 if the…

A: Total numbers 0 , 1 , 2 , 3 , 4  5 = 6

Q: 11. In how many ways can we seat 7 people at a round table with a certain 3 people not in…

A:

Q: How many three-digit numbers can be constructed from the digits 0, 1,2,3,4,5,6,8,9 if the number…

A: Given digits is0, 1, 2, 3, 4, 5, 6, 7, 8, 9Total no.of digits=10

Q: 2) How many numbers are there between 6000 and 7000 which have exactly one of their digits as 7?

A: Since, we have to find numbers between 6000 and 7000 so the thousand's place must be occupied by 6.…

Q: Assume that you are to select digits from the set {2,5,6,8,9} to form a number between 20 and 900.…

A: Assume that you are to select digits from the set {2,5,6,8,9} to form a number between 20 and 900.…

Q: Suppose that S is a finite set of positive integers. If the greatest integer in S is removed from S,…

A: Let the least integer in the set be y. Then the greatest integer in the set is y+72.  Let there are…

Q: 12. Suppose a list A contains the 30 students in a mathematics class, and a list B contains the 35…

A: list A(Mathematics)=30 studentslist B(English)=35 studentslist A∪B(Both)=20…

Q: 2.22 In a medical study, patients are classified in 8 ways according to whether they have blood type…

A: Given: Number of ways according to blood type =8 Number of ways according to blood pressure =3

Q: If A {100, 200, 300, 400, 500, 600} and B {200, 400, 600, 800}, find: AUB O {100, 200, 300, 400,…

A:

Q: Suppose that 40 Malaysian Chinese are surveyed and they speak at least one of the three dialects,…

A: This question is about set theory