.76 How many six-digit numbers with different digits belonging to the set ${0,1,2,3,4,5,5}$ and simultaneously: (a) divisible by 5 b) divisible by $25 ?

Q: how many integers from 1 to 1000 are multiples of 3 or 5 (or both)

A: We want to find number of integer from 1 to 1000 are multiples of 3 or 5 (or both)

Q: Let a and b be ranges of numbers in a number line such that –1 < a < 5 and 6 < b< 10. - If a is…

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Q: Three-digit numbers are formed from the digits 0,1,6,7,8 and 9 if no repitition is allowed d. how…

A: The given digits are 0, 1, 6, 7, 8, and 9.

Q: 3. Consider a set of numbers B = {n E Z|1<n< 900} Answer the following questions. (a) How many…

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Q: 1. How many 4-digit numbers can we make using the digits 3, 6, 0, 7 and 8 without repetitions? 2.…

A: 9) Solution: The word bracelet is symmetrical that is clockwise and anticlockwise arrangement are…

Q: In how many ways can you place 20 identical balls into five different boxes if each boxes has to…

A: Here we have to find 20 identical balls into five different boxes so that each box contain at least…

Q: In how many ways can 12 people line up in a row? 144 O 12 O 1212 479,001,600

A: Multiplication rule: If there are a ways of doing something and b ways of doing another thing, there…

Q: Find the number of elements in the set {o E S4lo (3) = 3}.

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Q: 4. How many combinations of 4 objects are there taken 2 at a time? O 12 O 24 O 6 2

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Q: Given the numbers 0, 1, 3, 5, 7, 8 and 9 and if repetition is allowed; a. How many 4-digit numbers…

A: 2.a.  There are 4 spaces in a 4-digit number. _ _ _ _ These 4 spaces needed to be fill using the…

Q: 2.36 (a) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each…

A: Given : Available digits are 0,1,2,3,4,5 and 6 Total of 7 digits are available Each digit can be…

Q: In how many ways can a bag of three identical balls and four identical coins be formed from a group…

A: Number of available balls = 12 Number of available coins = 12     Number of balls to be selected=3…

Q: (1) 2. Determine the total number of different outfits you can create from your closet if you have…

A: This is a problem related to permutation and combination. Based on the general formula and concept…

Q: 5. Show that for n attributes A, B, C, ...M. ... (ABC... M) ≥ (A) + (B) + (C) +. +(M)-(n-1) N, where…

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

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Q: If M = {distinct letters in the word mathematics} and N = {distinct letters in the word…

A: We will find out the required value.

Q: How many 3-digit numbers can be formed from the digits 2, 3, 4, 6, 7 without repetitions? b. How…

A: The 3-digit numbers that can be formed from the digits 2, 3, 4, 6, 7 without repetitions are: 234,…

Q: . a. How many distinct permutations can be made from the letters of the word “columns”?  b. How…

A: Given Word is "COLUMNS"No. of letters in word "COLUMNS" = 7

Q: 3.54. How many even five-digit numbers, in which all digits are different, can be formed from the…

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Q: nhow many nights may a watch of 4 men be arranged by a security agency om a crew of 16 so that no…

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Q: (d) If an order comes in for 10,000 steel rods, how many rods should the plant manager expect to…

A: We have given that,  For part (d) Let X be the random variable from normal distribution with mean…

Q: Consider five-digit numbers  = a1 a2 a3 a4 a5, with each digit from the set {1, 2, 3, 4}. a. How…

A: Solution is given as below:

Q: How many three-digit numbers can be formed under the following condition? The number is at least…

A: We have to find three - digit numbers that can be formed under condition  The number is at least 400…

Q: For how many n Ee {1,2, ..., 550} is n a multiple of one or more of 9, 4, or 7?

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Q: find the number of permutations of the letters in each word. a. florida b. arizona c. montana

A: a. The word “FLORIDA” contains letters. No letter is repeated. So, number of permutations of the…

Q: Q3/ How many three digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 such…

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Q: 6. How many integers from 1 through 100 must you pick in order to be sure of getting one that is…

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Q: 10. How many 6-digit numbers are even or are divisible by 5?

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Q: 2. If repetitions are not permitted, (i) how many 3-digit numbers can be formed from the six digits…

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Q: a) S, = In n=1

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Q: 2. Use a number line to visualize the following set: S = {n € R | 5 < n< 10}

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Q: In how many ways can a class of 14 students be assigned 3 A's, 2 B's, 2 C's, 3 D's and 4 F's? ways

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Q: d) In how many ways can you divide 28 persons into three groups having 4, 12 and 12 persons?

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Q: la) How many permutations are there of the word HOLIDAY? b) How many of these permutations do not…

A: Answer : a) There are 5040 permutations of the word HOLIDAY.  Total word in HOLIDAY = 7 Permutations…

Q: (e) How many integers are there from 1,0 through 9,99 (b) How many odd integers are there from 1,000…

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Q: 1. How many 4-digit numbers can we make using the digits 3, 6, 0, 7 and 8 without repetitions? 2.…

A: The following is the formula of making permutations by using any word is given by           Where N…

Q: Let A = {Dirk, Johan, Frans, Sarie}, B = {Frans, Sarie, Tina, Klaas, Henrika}, C = {Hans, Frans}.…

A: The given sets are as follows. A=Dirk,Johan,Frans,SarieB=Frans,Sarie,Tina,Klaas,HenrikaC=Hans,Frans…

Q: 3.50. How many three-digit numbers are there with different digits and at the same time: (a) odd b)…

A: Given problem Given that   How many three-digit numbers are there with different digits and at the…

Q: Refer to a bag containing 20 balls-six red, six green, and eight purple. In how many ways can we…

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Q: 3. Given that the digit 7,8,9,10, and 11. How many four digits numbers: (a) i. greater than 9000 can…

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Q: . How many four-digit numbers are there with different digits and simultaneously: (a) divisible by…

A: Given: Total number of digits = 10 (0 to 9) Number of digits in a number = 4

Q: How many odd numbers are there greater than 1,000 but less than 100,000? Select one: A. 49,050 B.…

A: Here we have to find the number of odd numbers which are greater than 1000 but less than 100000.…

Q: For n attributes A,, A2, --. , An (A, A2 . An) 2 (A,) + (A2) + .. + (A,)- (n - 1)N Where N is the…

A: To show that, For n attributes A1, A2,..... , An. (A1, A2,..... , An) ≥ (A1)+(A2)+...+(An)-(n-1)N…

Q: How many 8-digit numbers can be formed with the digits 3, 5, and 7? (b) What fraction of the…

A: a)The objective is to find how many 8-digit number is formed with the digits 3,5,and 7 the number of…

Q: a) How many three digit numbers are there that are not divisible by 5? b) there are 12 contestants…

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Q: in how many different ways can be letters of the word excel be arranged with two E's kept together

A: Given word is "EXCEL"letter 'E' is repeated =2 timesTotal no.of letters=5

Q: Let n(A) = 4, n(A ∩ B) = 4, n(A ∪ B) = 10. How many elements are there in B?

A: Given,  n(A) = 4, n(A ∩ B) = 4, n(A ∪ B) = 10

Q: How many ways to arrange a 4-digit number, provided that the said number must be even and there are…

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