At a benefit concert, eight bands have volunteered to perform but there is only

Question

At a benefit concert, eight bands have volunteered to perform but there is only enough time for five of the bands to play. How many lineups are possible?

An election ballot asks voters to select four city commissioners from a group of fifteen candidates. In how many ways can this be done?

Of 11 possible books, you plan to take 3 with you on vacation. How many different collections of 3 books can you take?

To win at LOTTO in one state, one must correctly select 7 numbers from a collection of 47 numbers (1 through 47 ). The order in which the selection is made does not matter. How many different selections are possible?

A textbook search committee is considering 12 books for possible adoption. The committee has decided to select 8 of the 12 for further consideration. In how many ways can it do so?

Explanation / Answer

1) Simplify

8!/3! = 8.7.6.5.4.3! / 3!
=6720
Therefore there are 6,720 lineups are possibe

2)

Let n = total of city commissioners
Let r = how many candidate are taken from the total
This is a combination question from probability math.
The formula you need is given by: nCr = n!/[(n - r)! * r!]

Let n = 15
Let r = 4

C(n,r)=C(15,4)C(n,r)=C(15,4)

=15!/(4!(154)!)

= 1365

3)  solve combinations, designate the number of items, 11, as n, and the number of items in a grouping, 3, as r.

nCr = n! / (n-r)!r! =11! / 3!(113)!) =165

Thus there are 165 different collections possible.

4) Use following Combination formula

nCr = n! / r!(n-r)!

n=47

r=7

=47!/(7!(477)!)

=62891499

5)

Use following Combination formula

nCr = n! / r!(n-r)!

=12! /(8!(12-8)!)

=495

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