Question

8. In many courts, 12 jurors are chosen from a pool of 30 perspective jurors.

a. In how many ways can 12 jurors be chosen from the pool of 30 perspective jurors?
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?

Answer 1

The number of ways to select 12 jurors are 86493225.

The number of ways to select 2 alternates are 306.

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
`^(n)C_(r)=(n!)/(r!(n-r)!)`

Substitute n=30 and r=12 in above formula.

`^(30)C_(12)=(30!)/(12!(30-12)!)`

`^(30)C_(12)=(30!)/(12!18!)`

`^(30)C_(12)=86493225`

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:
`^(n)P_(r)=(n!)/((n-r)!)`

Substitute n=18 and r=2 in above formula.

`^(18)P_(2)=(18!)/((18-2)!)`

`^(18)P_(2)=(18!)/(16!)`

`^(18)P_(2)=306`

Hence, the number of ways to select 2 alternates are 306.