Respuesta :
Answer:
The number of ways to select 12 jurors are 86493225.
The number of ways to select 2 alternates are 306.
Step-by-step explanation:
Consider the provided information.
In many courts, 12 jurors are chosen from a pool of 30 perspective jurors.
Part (A): In how many ways can 12 jurors be chosen from the pool of 30 perspective jurors?
Since order doesn't matter so we will use combination.
Use the formula for combination [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]
Substitute n=30 and r=12 in above formula.
[tex]^{30}C_{12}=\frac{30!}{12!(30-12)!}[/tex]
[tex]^{30}C_{12}=\frac{30!}{12!18!}[/tex]
[tex]^{30}C_{12}=86493225[/tex]
Hence, the number of ways to select 12 jurors are 86493225.
Part (B) Once the 12 jurors are selected, 2 alternates are selected. The order of the alternates is specified. If a selected juror cannot complete the trial, the first alternate is called on to fill that jury spot. In how many ways can the 2 alternates be chosen after the 12 jury members have been chosen?
Here 12 jury members have been chosen, so 30-12=18 perspective jurors are left.
From 18 perspective jurors we need to select 2 alternates.
Since the order of the alternates matter so we will use permutation:
The formula for permutation is: [tex]^{n}P_{r}=\frac{n!}{(n-r)!}[/tex]
Substitute n=18 and r=2 in above formula.
[tex]^{18}P_{2}=\frac{18!}{(18-2)!}[/tex]
[tex]^{18}P_{2}=\frac{18!}{16!}[/tex]
[tex]^{18}P_{2}=306[/tex]
Hence, the number of ways to select 2 alternates are 306.
