Question

Три мушкетёра Атос, Портос и Арамис вместе со своим другом дАртаньяном поссорились с пятью гвардейцами.Ссора кончилась одной дуэлью.Сколько существует способов выбрать противников для этой дуэли?

Answer 1

4*5=20 (сп) существует  способов выбрать противника для дуэли 
ответ:  20 способов 

Answer 2

Number of ways to choose opponents for the duel

To determine the number of ways to choose opponents for the duel between Athos, Porthos, Aramis, and d'Artagnan and the five guards, we can use the concept of combinations.

In this scenario, we have a total of 5 guards and 4 musketeers. The number of ways to choose opponents for the duel can be calculated using the combination formula:

nCr = n! / (r! * (n-r)!)

Where: - n is the total number of guards and musketeers (5 + 4 = 9) - r is the number of musketeers (4)

Plugging in the values, we get:

9C4 = 9! / (4! * (9-4)!)

Simplifying the equation:

9C4 = 9! / (4! * 5!)

Using the factorial notation, we can further simplify:

9C4 = (9 * 8 * 7 * 6 * 5!) / (4! * 5!)

Cancelling out the common terms:

9C4 = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1)

Calculating the values:

9C4 = 126

Therefore, there are 126 ways to choose opponents for the duel between the musketeers and the guards.