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 consecutive positions?

Q: Find the least amount of different numbers to pick from positive integers that are at most 100 to…

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Q: Without repeating any digits, how many 3-digit numbers can be formed from the 5 digits {1,2,3,4,5}…

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Q: if x1  + x2  + x3 +x4  x5 +x6= 82 and xi >= 3  and 1<= i <= 6   find combinations with repetition of…

A: The number of integer solution vectors to the equation  ∑k=1nxk=t , for each xk≥a the number of…

Q: How many three-number combinations are possible on a combination lock having 40 numbers on its dial…

A: We have , total 40 number on dial and we have to find the combination lock of 3 digits. Since , the…

Q: How many 10 digit real even number can be created (It cannot start with a 0) with 5 zeroes and 5…

A: Basic concepts of making combination are used. Information given, As we have only two choices of…

Q: the final exam score is higher. If a student's four test scores are 81, 65, 34, and 88, what is the…

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Q: If student 10 is not selected, then student 5 should be selected how can I represent this constrain…

A: Given If student 10 is not selected, then student 5 should be selected

Q: Which represents equal sets?. O A EB and BEA O IAI-IBI O All numbers in Set A are in Set B. O MCNand…

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Q: How many ways that two girls and 4 boys can fall in a line of there must be a girl and a boy in the…

A: Let us assume there are three persons A, B and C sitting beside each other. The different ways in…

Q: let a,b,c,d,e and f be different positive integers so that a² - b² = c² - d² = e² - f² = 63. Value a…

A: Given:- a,b,c,d,e and f are different positive integers.  also a2-b2=c2-d2=e2-f2=63. To find :- the…

Q: Prove that a three-digit number is a multiple of 9 whenever the sum of the digits is a multiple of…

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Q: How many ways that two girls and 4 boys can fall in a line of there must be a girl and a boy in the…

A: Introduction: There are 2 girls, and 4 boys.

Q: How many codes fit this description?

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Q: Show that 2 + V5 is imational number

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Q: Find the set of all positive integers n with the property that the set  M={n,n+1,n+2,n+3,n+4,n+5}…

A: A very good problem based on a nice application of quadratic residues

Q: Each card in a standard deck of cards has a rank and a suit. The cards are ranked from 2 to 10,…

A: Part (4) Out of 52 cards, 26 cards are blacks. Therefore, the number of black cards is 26. Then, the…

Q: The house of a row are numbered consecutively from 1 to 49 .show that there is a value of x such…

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Q: bank PIN is a string of four digits, each digit 0-9. How many choices are there for a PIN if the…

A: Given A bank PIN is a string of four digits, each digit 0-9. Odd numbers=1,3,5,7,9

Q: How many strings of three decimal digits (each digit can be 0-9) do not contain the same digit three…

A: Solution :-

Q: A committee of seven Congressmen will be selected from a group of seven Democrats and four…

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Q: How many four digit codes can be made out of the digits 0,2,4and 8 if the repetition of digits is…

A: We have to find four digit codes can be made out of the digits 0,2,4and 8 ....

Q: a) How many four-digit numbers can be formed from the digit 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each…

A: a.  Here the numbers are 0,1,2,3,4,5,6,7,8,9 n=10 We need to make a 4 digit number and there is no…

Q: find the number of six-digit positive integers whose digits sum to 30   the answer is C(34,5) -…

A: We shall illustrate the method involved. The details are provided in step 2.

Q: Suppose that a1, a2, a3, a4, a5 are five numbers. 5 If ak =-7 then (2ak + 3) is equal to... k=1 k=1

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