O Given 20 balls of different colors and 10 bananas, find the number of ways to distribute i-The 20 balls to 6 children such that everyone gets at léast one. ii- The 10 bananas in 3 identical boxes such that in each bôx at least one.

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Q: Assume that the committee consists of 10 Republicans and 5 Democrats. A subcommittee consisting of 5…

A: Given Information: Assume that the committee consists of 10 Republicans and 5 Democrats. A…

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Q: Suppose that an experimenter tossed three balanced coins. He defined X₁, to denote the number of…

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Q: In a class of 130 SHS students, 41 offers agricultural science, 62 offers business and 31 offers…

A: 1.     Only A is 41-16=25 Only B is 62-16-14=32 Only V is 31-14=17   Venn diagram-

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A: Given 4 types of fruit (apple, banana, orange and peach)

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Q: A box contain 8 red and 6 green balls. In how many ways can 3 balls be drawn such that 2 is red and…

A: GivenA box containNo.of red balls = 8No.of green balls = 6Total no.of balls = 14

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A: The given letters are j, k, l, m, n, o and p. 4 letters are taken at a time.

Q: A box contains 18 red, 7 green, 11 blue, 21 yellow and 5 white balls. what is the minimum number of…

A: Given that a box contains 18 red, 7 green, 11 blue, 21 yellow and 5 white balls.

Q: XI In a group of 11 boys and 9 girls, 5 are to be selected. In how many ways can they be selected…

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Q: 5. Is it possible to plant 10 trees in 10 straight rows, with 3 trees in each row? Hint: Desargues…

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Q: Out of 150 students of a college, 38 qualified for M.C.A., 41 qualifies for M.B.A. ad 38 qualified…

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Q: When we are considering n objects taken r at a time, with r . 1, why will the number of combinations…

A: "When we are considering n objects taken r at a time, with r . 1, why will the number of…

Q: A rectanglular table seats 6 people; I person on each end and 2 on each of the longer sides. Thus,…

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Q: e) True or False: If 25 oranges are placed into 22 baskets, then at least one basket must contain at…

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Q: How many ways. row if none ave there for n COUPICS to sit sit together. of the couples in a

A: We have n couples , that is, 2n people in total. Number of ways to seat n couples , so that the…

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A: In theory of combinatorics, the way of selecting r objects from n objects with regard to the order…

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A: There are 5 colleges and I want to meet at least 8 from the same college.  Let us think of a case…

Q: A box has (4) balls. Choose (2) balls one by one with replacement, x is the first chosen and Y is…

A: Given information: No. of balls=4Selection=with replacementNo. of balls to be selected=2

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Q: Alice has 10 balls (all different). First, she splits them into two piles; then she picks one of the…

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Q: Of 12 pounds of salt water 10% is salt; of another mixture 3% is salt. Howmany pounds of the second…

A: Let x pounds of the second should be added.  So total amount of the mixture = (x+12) pounds    10%…

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A: Follow the steps.

Q: AMong the seven nominees for two VaGancies on the city council are three Men and four women. In how…

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Q: 3. How many ways are there to distribute n identical balls in k distinguishable (labelled) boxes…

A: It is given that there are n identical balls in k distinguishable boxes.

Q: An urn contains 6 green balls and 7 red balls. A man selects balls at random without looking at…

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Q: Find the number of permutations using 4 different letters a, b, c, and d, if they are taken 2 at a…

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Q: Twelve teachers are to be assigned to three schools. In how many ways can this be done if: i. a…

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Q: 8. In a fruit feast among 200 students, 88 chose to eat durians, 73 ate mangoes, and 46 ate litchis.…

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Q: How many ways are there for 8 men and 5 women to stand in a line, so that no two women stand next to…

A: The number of ways to arrange n objects in a queue is obtained using the formula n!. The number of…

Q: Consider the word TORTOISE. Count the number of arrangements of this word (a) such that no two…

A: Consider the given word TORTOISE. The objective is to count the number of arrangements of this word:…

Q: A2. a. A company decided to distribute 5 identical computers among its employees. In how many…

A: The number of identical computers is 5. The number of distinct people is 3. Since, each employee…

Q: How many times would you expect to roll a fair die before all 6 sides appeared at least once? (Hint:…

A: Consider Yi be the number of additional rolls required for a new side to appear until i-th side have…

Q: salesperson is scheduling 5 meetings in one day. In how many different ways can the salesperson…

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Q: 4. How many different arrangements are there of the letters in the word "success" and how many have…

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Q: Suppose you are asked to arrange 10 books in a shelf. Three of them are Mathematics, 4 are English…

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

Q: Two coins are tossed simultaneously, find the prob (i) at least one head (ii) at most one head (iii)…

A: For this case, the number of possible of outcomes will be: (HH), (HT), (TT), (TH) Here, H represents…

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A: To find all the permutations of the 4 objects a ,b, c, and d, taken 3 at a time.

Q: Alice has 10 balls (all different). First, she splits them into two piles; then she picks one of the…

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Q: There are 5 pocket holes at the periphery of a round horizontal platform. In how many ways can 5…

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Q: In how many ways can you distribute 10 identical balls between Ram, Yuvraj Singh, Mansoor and…

A: Number of way of choosing r objects out of n identical objects =Crn=n!(n-r)!×r!Given:total identical…