Question
In: Statistics and Probability
A certain lottery works this way: The player selects 5 different numbers from 1 to 40....
A
certain lottery works this way: The player selects 5 different
numbers from 1 to 40. To win, the player must correctly match all
five numbers. The winning numbers are drawn one at a time, and
cannot be reused. If you could list all possible outcomes in the
sample space, how many outcomes would you have?
Solutions
Expert Solution
We have to select 5 different numbers from numbers 1 to 40 .
The Sample Space is the total number of ways in which 5 numbers can be drawn.
Since, the order of selection of numbers doesn't matter,This is a Combination.
And NO REPETITION is Allowed .
TASK: Choose 5 numbers from 40 numbers
FORMULA is :
Here, n= 40 r= 5
Therfore, Total Number of Outcomes= 
= 
=
= 
=
( 35! gets cancelled from Numerator and Denominator)
5! = 5*4*3*2*1 =120
=1*13*38*37*36
= 658008
Therefore,there are 658008 possible outcomes in the sample space.
C(n,r) = "C= = n! r!(n-r)!
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