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18. A woman has 10 close friends. Find the number of ways in which she can invite 4 of them to dinner if

18. A woman has 10 close friends. Find the number of ways in which she can invite 4 of them to dinner if

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.7: Introduction To Coding Theory (optional)
Problem 18E
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Solve Q18a, b & c Showing detailly all steps

Find the number of ways in which a committee of 5 can be selected form the group if either A or B but not both must be a member of the committee. 5. Recently in Cameroon, car numbers in the ten province in which the car is registered; followed by three digits taken form the digits 0 to 9 inclusive which must not all be zeros then two letters each taken form the 26 letters of the alphabet starting with the pair AA to end with ZZ e.g OU 202AB, LT 439 MM etc. find the maximum number of cars that can be registered by this system (r+1)! (r+1)! Y6. Given thatr>1, r EN, simplify (r-1)! 140 Hence evaluate E1 (r-1)! 11) A rural council commission of 6 members is to be selected form 10 men and 7 women. Find the number of ways in which this can be done if a) The commission must consist of 4 men and 2 women, b) The commission is to include at least 4men and at least 1 woman V17. A handball team of 7 players is to be selected from a group of 15 players in which there are two brothers. Find the number of ways in which the team can be selected if a) The two brothers must be included in the team b) At most one of the two brothers is to be included in the team. 18. A woman has 10 close friends. Find the number of ways in which she can invite 4 of them to dinner if a) Each of the is equally likely to attend, b) Two of the friends are married and will not attend separately 6c) Two of them are not on speaking terms and will not attend together.
Transcribed Image Text:Find the number of ways in which a committee of 5 can be selected form the group if either A or B but not both must be a member of the committee. 5. Recently in Cameroon, car numbers in the ten province in which the car is registered; followed by three digits taken form the digits 0 to 9 inclusive which must not all be zeros then two letters each taken form the 26 letters of the alphabet starting with the pair AA to end with ZZ e.g OU 202AB, LT 439 MM etc. find the maximum number of cars that can be registered by this system (r+1)! (r+1)! Y6. Given thatr>1, r EN, simplify (r-1)! 140 Hence evaluate E1 (r-1)! 11) A rural council commission of 6 members is to be selected form 10 men and 7 women. Find the number of ways in which this can be done if a) The commission must consist of 4 men and 2 women, b) The commission is to include at least 4men and at least 1 woman V17. A handball team of 7 players is to be selected from a group of 15 players in which there are two brothers. Find the number of ways in which the team can be selected if a) The two brothers must be included in the team b) At most one of the two brothers is to be included in the team. 18. A woman has 10 close friends. Find the number of ways in which she can invite 4 of them to dinner if a) Each of the is equally likely to attend, b) Two of the friends are married and will not attend separately 6c) Two of them are not on speaking terms and will not attend together.
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