How many numbers must be selected from the set {1, 2, 3, 4, 5, 6, 7, 8} to guarantee that at least one pair of these numbers add up to 9?

Q: How many distinct ten-digit passwords are possible if you must use at least one 26 lower case letter…

A: Given: you must use at least one 26 lower case letter from {a, b, . . . , z}, at least one 26 upper…

Q: How many strings of length 5 can be formed if the alphabet (set of available characters)is {a,b,c}…

A: When there are nth places and m elements. With repetition, the choice of 1st place will be m, the…

Q: How many numbers greater than 3000 can be form with the digits 0,2,3,4 a.  if repetition is not…

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Q: How many subsets does the set  F = {4, 5, 6, 7, 8}  have?

A: Given : F = 4, 5, 6, 7, 8

Q: 5 identical copies of a movie will be stored on 20 computers such that each computer has at most 1…

A: Given: 5 identical copies of a movie will be stored on 20 computers

Q: How many strings of 1our decimal digits have all four digits that are different? How many strings of…

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Q: In a set of 2 positive integers, how many ways it can be chosen in less than 50? 1.

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Q: Each student at State College has a student I.D. number consisting of seven digits (the first digit…

A: no.of digits ( 0 to 9)=10no.of letters(A,B,C,D,E)=5

Q: Each student at State College has a student I.D. number consisting of five digits (the first digit…

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Q: a) How many different license plates are possible if each contains 2 letters​ (out of the​…

A: We solve this question by using permutations If characters are not repeated then the total number of…

Q: How many ways are there to list the digits {1,2, 2, 3, 4, 5, 6} so that identical digits are not in…

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Q: Each student at State College has a student I.D. number consisting of eight digits (the first digit…

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

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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: The digits 0, 1, 2, 3, 4, 5, 6 and 7 are used to make 4 digit codes. (a) How many unique codes are…

A: As per Bartleby guideline, if more than three subparts are asked only first three to be answered…

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: How many pairs of two distinct integers chosen from the set {1, 2, 3,..., 101} have a sum that is…

A: Since you have posted multiple questions and we can answer one question. So answer provided for the…

Q: How many ways are there to select three unordered elements from a set with five elements when…

A: Given: Number of elements = 5 Number of unordered elements = 3 If repetition is allowed,…

Q: a set of marbles consisting of 4 red, 3 green, 2 blue, 3 orange, 2 yellow and 3 purple marbles. How…

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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: A multiset is similar to a set, but can contain an element more than once. How many multisets can we…

A: You can identify every multiset with an ordered pair of usual sets, call them high and low. If you…

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: How many subsets are there of the set N = {5, 42}?

A: We ahave to find no. Of subsets.

Q: How many strings of ten lowercase letters from the English alphabet contain the lette consecutive…

A: String contains total 10 lowercase letters

Q: How many subsets does the set  F = {3, 4, 5, 6, 7} have?

A: No. of subsets in a set: The number of subsets in a set containing n elements is given by 2n. No. of…

Q: A license plate consists of   five symbols on each​ plate, where the first two symbols are letters…

A: Fundamental principle of counting : If an event occur in m ways an corresponding to it another event…

Q: Let S={1,2,3,4,5,6,7,8,9,10,11}   How many subsets contain at least one odd number?

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Q: Each student at State College has a student I.D. number consisting of eight digits (the first digit…

A:

Q: How many subsets of set S = {1, 2, 3, 4, 6} do not contain odd numbers? Use bijection to solve this…

A: Solution S={1,2,3,4,6}

Q: How many ways are there to list the digits 1, 1, 2, 2, 3, 4, 5 so that the digit 3 and 4 are not in…

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Q: How many pairs of two distinct integers chosen from the set {1, 2, 3, 101} have a sum that is even?

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Q: A product code consists of a string of 4 different letters selected from the set {S,T,U,V,W,X}. How…

A: The number of ways to arrange r objects selected from n distinct objects is given by the permutation…

Q: How many strings of 12 ternary digits (0, 1, or 2) are there that contain exactly hree Os, five 1s,…

A: Strings of 12 ternary digits, 3 possibilities for each digit in the string, gives a total of 3^12 =…

Q: Using the pigeonhole principle How many numbers must be selected from the set {1, 3, 5, 7, 9, 11,…

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Q: Each student has an ID number consisting of 5 digits ( the first digit is non-zero, and digits can…

A: Number of digits in the ID number = 5 Since first digit is non-zero, the number of possibilities for…

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: How many different 3-digit numbers are possible using only the digits 1,5,6,7,8 ? How many…

A: We have to find no of ways for make 3 and 4 digit numbers  when repetition allow and not allowed

Q: 10 identical copies of a movie will be stored on 40 computers such that each computer has at most 1…

A: Given the statement. 10 identical copies of a movie will be stored on 40 computers such that each…

Q: How many elements are in the set {0, {0}}?

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

A: According to the given information in this question We need to find the value of C(8,4)

Q: How many strings of eight uppercase English letters are there that start and end with X, if letters…

A: In English Alphabet we have 26 letters. We have to make a string of 8 uppercase English Letters.…

Q: Show that if any 14 numbers are selected from the set S = {1,2,3,...,25}, [14] there are at least…

A: Note that the numbers in each of the first twelve sets sum to 26, and that there is no pair of…

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: 2) How many elements are in the union of 5 sets if the sets contain 10,000 elements, each pair of…

A: Given that there are 5 sets and sets contains 10,000 elements, each pair of sets has 1000 elements,…

Q: If you have 12 boxes then how many balls do you have to put randomly into the boxes in order to…

A: Given that, We are having 12 boxes. In order to have atleast 4 balls in each box when a random box…

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: Consider 4 digit numbers with each digit from the set {1, 2, 3, 4, 5, 6, 7, 8, 9} .  How many such…

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Q: A natural number greater than 1 that is divisible by a number other than itself and 1 is called a/an…

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Q: We are making 5-letter words from the set of letters a, b, c, d, e, f..., in such a way that we have…

A: Here we will use permutation /arrangement and combination / selection  Number of way r object can be…