The number of different ways of choosing 4 items from a group of 9 items is simply:#((9),(4)) = (9!)/(5!4!) = 126# Show
(b) You have already chosen 2 of the committee so you are now looking at choosing the remaining 2 from a group of 7: #((7),(2)) = (7!)/(5! 2!) =21# (c) For all committees that has John onboard, you need to choose 3 more, but you are choosing from a group of 7 as Barbara cannot be on the same committee. So in that scenario you have#((7),(3)) #ways of doing it. The same applies if Barbara is to be on the committee and John excluded. So, overall, the total number of ways to do this is: #2 xx ((7),(3)) = (2 xx 7!)/(4!3!) = 70# Answer link EZ as pi Apr 17, 2017 #A) 126#different committees Explanation:Recall: The number of different ways of arranging#n#numbers is#n!# If 4 people are to be selected from 9 people: This gives#9xx8xx7xx6#different committees, however this will include the same combinations of people. A) Therefore, for 4 people chosen from 9 there are #(9xx8xx7xx6xx5)/(4xx3xx2xx1) = 126#different committees. B) If two people must stand, there are 2 people to be chosen from the remaining 7. Applying the same thinking as above this gives: #(7xx6)/2 =21#different committees. C) if either one or the other must stand there are then 3 people who must be chosen from the remaining#7#people; The term “combination” is thrown around loosely, and usually in the wrong way. Things like, “Hey, what’s the suitcase lock combination?” are said But what one really ought to be saying is “Hey, what’s the suitcase lock permutation?” So what’s the difference? And what exactly are a permutation and combination? They are two very different terms. Let’s learn about them in detail, PermutationA permutation is an act of arranging objects or given quantity maybe numbers from a group of objects or collection given in a particular order as per given conditions. Example – How many 2 letter words are there that can be formed by using the letters in the word LATE? Answer is 4P2 (pronounced as 4 p 2) = 4!/(4 – 2)! = 4!/(2)! = (4 × 3 × 2 × 1)/(2 × 1) = 24/2 = 12. CombinationThe combination is the way of selecting the objects or given quantity maybe numbers from a group of objects or collection from a group of objects or collection, in such a way that the order of the objects does not matter. For example – how many groups of 2 people can be selected from 4 people? Answer – 4 C 2(pronounced as 4 C 2) = 4!/(4 – 2)!(2)! = 4!/(2)!(2)! = (4 × 3 × 2 × 1)/(2 × 1)(2 × 1) = 24/4 = 6. The formula for permutations and combinations
Find the number of committees of the size of 4 formed from 8 people.Answer:
Similar ProblemsQuestion 1: Find the number of committees of the size of 3 formed from 5 people. Answer:
Question 2: How many different committees of 3 members can be chosen out of 5 people in a group so that one particular person is always chosen? Answer:
Question 3: How many committees of 5 consisting of 3 men and 2 women can be formed from 8 men and 6 women? Answer:
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