Question

1. Из 20 солдат необходимо выделить наряд из 3-х солдат. Сколькими способами это можно сделать?

Answer 1

(20*19*18)/3!=6840/6=1140 способов

Answer 2

Calculation of the Number of Ways to Select a Squad of 3 Soldiers from a Group of 20 Soldiers

To calculate the number of ways to select a squad of 3 soldiers from a group of 20 soldiers, we can use the concept of combinations. In mathematics, a combination is a selection of items from a larger set without regard to the order of the items.

The formula to calculate the number of combinations is given by:

C(n, r) = n! / (r! * (n - r)!)

Where: - n is the total number of items in the set (in this case, the total number of soldiers) - r is the number of items to be selected (in this case, the number of soldiers in the squad)

Let's calculate the number of ways to select a squad of 3 soldiers from a group of 20 soldiers using the formula:

C(20, 3) = 20! / (3! * (20 - 3)!)

Simplifying the equation:

C(20, 3) = 20! / (3! * 17!)

Now, let's calculate the value:

C(20, 3) = (20 * 19 * 18) / (3 * 2 * 1) = 1140

Therefore, there are 1140 different ways to select a squad of 3 soldiers from a group of 20 soldiers.