4280561376 group of interviews can be made
Solution:
Given that,
42 citizens called for jury duty. Eleven are randomly chosen to for the interview phase
Therefore, we can say, out of 42 citizens, 11 are randomly selected
This is a combination problem
A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected.
The formula for combination is given as:
[tex]n C_{r}=\frac{n !}{(n-r) ! r !}[/tex]
where n represents the total number of items, and r represents the number of items being chosen at a time
Here, n = 42 and r = 11
Substituting them in formula,
[tex]42 C_{11}=\frac{42 !}{(42-11) ! 11 !}[/tex]
[tex]42 C_{11}=\frac{42 !}{31 ! 11 !}[/tex]
For a number n, the factorial of n can be written as,
[tex]n !=n \times(n-1) \times(n-2) \times \ldots .2 \times 1[/tex]
Therefore, the above expression becomes,
[tex]42 C_{11}=\frac{42 \times 41 \times 40 \times \ldots . \times 2 \times 1}{31 \times 30 \ldots . . \times 1 \times 11 \times 10 \ldots . \times 1}[/tex]
[tex]42 C_{11}=\frac{42 \times 41 \times \ldots . \times 32}{11 \times 10 \times \ldots \times 1}[/tex]
[tex]42C_{11} = 4280561376[/tex]
Thus 4280561376 group of interviews can be made
