Answer:
a. 7893600
![b.\ \dfrac{1}{26}](https://tex.z-dn.net/?f=b.%5C%20%5Cdfrac%7B1%7D%7B26%7D)
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
25
24
23
22 = <em>7893600</em>
b. Probability of winning by choosing one number:
Formula for probability of an event E can be observed as:
![P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}](https://tex.z-dn.net/?f=P%28E%29%20%3D%20%5Cdfrac%7B%5Ctext%7BNumber%20of%20favorable%20cases%7D%7D%7B%5Ctext%20%7BTotal%20number%20of%20cases%7D%7D)
Number of favorable cases = 1
Total number of cases = 26
So, required probability:
![P(E) = \dfrac{1}{26}](https://tex.z-dn.net/?f=P%28E%29%20%3D%20%5Cdfrac%7B1%7D%7B26%7D)
So, the answers are:
a. 7893600
![b.\ \dfrac{1}{26}](https://tex.z-dn.net/?f=b.%5C%20%5Cdfrac%7B1%7D%7B26%7D)