In a certain lottery, you must select 5 numbers (in any order) out of 26 correctly to win. a. How many ways can 5 numbers be chosen out of 26 numbers? b. You purchase one lottery ticket. What is the probability of winning? a. There are nothing different ways the numbers can be selected.

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Respuesta :

isyllus isyllus · Answer 1 · 2020-07-03T04:29:18+02:00

Answer:

a. 7893600

[tex]b.\ \dfrac{1}{26}[/tex]

Step-by-step explanation:

Given that there are 26 numbers out of which 5 numbers are to be chosen.

Here repetition is not allowed.

For each of the 5 cases, the total number of possibilities will keep on decreasing by 1.

1st case, number of possibilities = 26

2nd case, number of possibilities = 25

3rd case, number of possibilities = 24

4th case, number of possibilities = 23

5th case, number of possibilities = 22

a. Total number of possibilities = 26 [tex]\times[/tex]25 [tex]\times[/tex]24 [tex]\times[/tex]23 [tex]\times[/tex]22 = 7893600

b. Probability of winning by choosing one number:

Formula for probability of an event E can be observed as: [tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

Number of favorable cases = 1

Total number of cases = 26

So, required probability:

[tex]P(E) = \dfrac{1}{26}[/tex]

So, the answers are:

a. 7893600

[tex]b.\ \dfrac{1}{26}[/tex]