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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orchestra answered 1 year ago
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