A certain club is forming a recruitment committee consisting of five of its members. They have calculated that there are 8,568 different ways to form such a committee. The club has two members named Jack and Jill. They have calculated that 2,380 of the potential committees have Jack on them,2,380 have Jill, 1,820 have Jack but not Jill, 1,820 have Jill but not Jack, and 560 have both Jack and Jill.Let U be the set of all possible committees of five that can be formed; let A be the set of these committees that have Jack on it, let B be the set of these committees that have Jill on it. Represent the above given information using set cardinality, for example:|U |=8,568How many committees have either Jack or Jill on it?How many committees have neither Jack nor Jill on it?Jack and Jill are car-pooling, so they insist that IF either one is on the committee, the other person must also be on the committee. How many committees meet this condition?Jack and Jill have had a fight. Jack says, "If Jill is on the committee, I won't be." Jill says, "Likewise." How many committees meet this condition?

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Asked Sep 19, 2019
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  1. A certain club is forming a recruitment committee consisting of five of its members. They have calculated that there are 8,568 different ways to form such a committee. The club has two members named Jack and Jill. They have calculated that 2,380 of the potential committees have Jack on them,

2,380 have Jill, 1,820 have Jack but not Jill, 1,820 have Jill but not Jack, and 560 have both Jack and Jill.

  1. Let U be the set of all possible committees of five that can be formed; let A be the set of these committees that have Jack on it, let B be the set of these committees that have Jill on it. Represent the above given information using set cardinality, for example:

    |U |=8,568

  2. How many committees have either Jack or Jill on it?

  3. How many committees have neither Jack nor Jill on it?

  4. Jack and Jill are car-pooling, so they insist that IF either one is on the committee, the other person must also be on the committee. How many committees meet this condition?

  5. Jack and Jill have had a fight. Jack says, "If Jill is on the committee, I won't be." Jill says, "Likewise." How many committees meet this condition?

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Expert Answer

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Step 1

Consider the given information are

  1. Let U be the set of all possible committees of five that can be formed.
  2. let A be the set of these committees that have Jack on it
  3. let B be the set of these committees that have Jill on it
Step 2

Let there are total member in the club = n

Then selecting 5 member from the n people is 8568 then

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n! "С, = 8568 51(п-5)! п(п-1) (п-2)(п-3)(п-4) (п-5)_ss68 51(п-5)! п(п-1)(п-2)(п-3) (n-4) -1028160

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Step 3

Solving this we will get n=18

Hence there are tot...

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Math

Algebra

Permutations and Combinations