Question

КОМБИНАТОРИКА! Среди 20 участников разыгрывается 3 приза (Приз 1, Приз 2, Приз 3). Каждый участник может выйграть только один приз. Сколько есть возможностей ?

Answer 1

На 1 приз может претендовать только 20 участников. На 2-19, на 3- уже 18. Итого 20*19*18=6840 комбинаций.

Answer 2

Combinatorics: Number of Possibilities for Prize Distribution

To determine the number of possibilities for distributing the 3 prizes among the 20 participants, we can use the concept of combinations. Since each participant can win only one prize, we need to calculate the number of ways to choose 3 participants out of 20 to receive the prizes.

The formula for calculating combinations is given by:

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

Where: - n is the total number of participants (20 in this case) - k is the number of participants to be chosen to receive the prizes (3 in this case) - ! denotes the factorial operation, which means multiplying a number by all positive integers less than it down to 1.

Using this formula, we can calculate the number of possibilities as follows:

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

Now, let's calculate the result:

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

Therefore, there are 1140 possible ways to distribute the 3 prizes among the 20 participants.