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A town council consists of 8 members including the mayor.
How many different committees of 4 can be chosen from this council?

Respuesta :

tressie
you would use combination in this so it would be 8C4 because the order doesnt matter in this case.

so 8c4 = 8! = 8*7*6*5*4<- This is the
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(8-4)!*(4!) (4!)*4*3*2*1 the factoral 4! that will cancelled out 4 on top which will leave 8*7*6 on top and 4*3*2*1 [ 8*7*6. ]
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[ 4*3*2*1 ] on the bottom...which you will calcuate the result and simplify it if needed

Number of different committees that can be chosen is equal to [tex]\boldsymbol{70}[/tex]

Permutations and combinations

A permutation is the process of putting things or numbers in a particular order.

Combinations are a method of picking objects or numbers from a collection or set of objects in the same cluster that the ordering of the objects doesn't really matter.

Total number of members [tex]=8[/tex]

Number of members chosen [tex]=4[/tex]

So,

Number of different committees that can be chosen [tex]=\boldsymbol{\binom{8}{4}}[/tex]

                                                                                 [tex]=\frac{8!}{4!4!}\\=\boldsymbol{70}[/tex]

Find out more information about permutations here:

https://brainly.com/question/1216161?referrer=searchResults

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