The probability for one person to take a job is 0.0714.
Explanation:
This can be calculated using the combination formula:
C(n, r) = n! / (r! * (n - r)!)
where:
n = the total number of items
r = number of items to be chosen.
Next, calculate C(9, 3):
C(9, 3) = 9! / (3! * (9 - 3)!)
= 9! / (3! * 6!)
= (9 * 8 * 7) / (3 * 2 * 1)
= 84
So, there are 84 different ways to choose 3 persons out of 9.
Since each person can take one job only, the first job may be given to any of the 9 persons.
The second job might be assigned to any of the 8 remaining persons, The third job can be assigned to any of the remaining 7.
Number of favorable outcomes: 9 * 8 * 7 = 504
Probability for one person to take a job:
Probability = Favorable outcomes / Total outcomes
504 / 84
= 6/84
= 0.0714