Find the numerical value.
-Your manager will assign her 9 employees to three tasks, 2 to task A, 4 to task B, and 3 to task C. If she randomly assigns employees to tasks, what is the probability that you and your best friend
Will be the two assigned to task A?
A) $\frac { 2 } { 9 }$
B) $\frac { 1 } { 1260 }$
C) $\frac { 1 } { 512 }$
D) $\frac { 1 } { 36 }$

Question

Find the numerical value.
-Your manager will assign her 9 employees to three tasks, 2 to task A, 4 to task B, and 3 to task C. If she randomly assigns employees to tasks, what is the probability that you and your best friend
Will be the two assigned to task A? 
A) $\frac { 2 } { 9 }$
B) $\frac { 1 } { 1260 }$
C) $\frac { 1 } { 512 }$
D) $\frac { 1 } { 36 }$

Quizplus · Accepted Answer

The probability is calculated by dividing the favorable outcomes by the total possible outcomes. For you and your friend to be assigned to task A, there's only 1 favorable outcome. The total ways to assign 9 employees to the tasks are calculated by the combination formula, which is $\frac{9!}{2!4!3!}$ for the groups of 2, 4, and 3 respectively. This equals 1260. Thus, the probability is $\frac{1}{1260}$, but due to a mistake in my calculation process, the correct interpretation of the choices given leads to the realization that the intended correct answer and explanation do not match any of the provided options correctly. The correct calculation for the probability of you and your friend being chosen for task A out of 9 people, with the specific distribution of tasks, should indeed involve combinations but the explanation provided does not accurately lead to any of the choices given. The correct approach involves choosing 2 people out of 9 for task A (which is you and your friend, so it's a 1 in $\binom{9}{2}$ chance), and then the rest of the tasks are irrelevant since the question only asks about the probability of you two being chosen for task A. The calculation should be $\frac{1}{\binom{9}{2}} = \frac{1}{36}$, making D the correct answer. My initial explanation mistakenly calculated the total arrangements without focusing solely on the selection for task A.

Find the Numerical Value 29\frac { 2 } { 9 }92​

Find the Numerical Value $\frac { 2 } { 9 }$