Question 1191355
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One state’s lottery consists of a person choosing 5 different numbers, each between 1-50. 
Find the probability of matching all five numbers if…
a) order matters
b) order does not matter
*Please use the P(A)=number of outcomes in event A/total numbers of outcomes formula*
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<pre>
(a) If the order matters, then 

        total numbers of outcomes = 50*49*48*47*46 = 254251200    

            (the product of 5 consecutive integer numbers in descending order, starting from 50);


        number of favorable outcomes = 1.

        The probability is  P = {{{1/254251200}}}.    <U>ANSWER</U>




(b)  If the order does not matter, then

        total numbers of outcomes = {{{C[50]^5}}} = {{{(50*49*48*47*46)/(1*2*3*4*5)}}} = 2118760  

            (the number of combinations of 50 items taken 5 at a time);


        number of favorable outcomes = 1.

        The probability is  P = {{{1/2118760}}}.      <U>ANSWER</U>
</pre>

Solved.