Question

Пассажирский поезд состоит из трёх багажных вагонов и восьми купированных.Сколькими способами сформировать состав, если багажные вагоны должны находиться в его начале?

Answer 1

Решение в приложении.

Answer 2

Calculation of Possible Combinations

To determine the number of ways to form a train composition with three baggage cars at the beginning, we can use the concept of permutations and combinations.

Since the order of the cars matters (the baggage cars must be at the beginning), we need to calculate the number of permutations. We have three baggage cars and eight compartment cars, so the total number of cars is 3 + 8 = 11.

The number of ways to arrange the cars is given by the formula for permutations:

P(n, r) = n! / (n - r)!

Where: - n is the total number of cars (11 in this case) - r is the number of baggage cars (3 in this case) - ! denotes the factorial operation

Substituting the values into the formula, we get:

P(11, 3) = 11! / (11 - 3)!

Simplifying the expression:

P(11, 3) = 11! / 8!

Now, let's calculate the value using the factorial function:

P(11, 3) = (11 * 10 * 9 * 8!) / 8!

The factorials in the numerator and denominator cancel out, leaving us with:

P(11, 3) = 11 * 10 * 9 = 990

Therefore, there are 990 different ways to form the train composition with three baggage cars at the beginning.