Question

To celebrate the five-year anniversary of a consultancy specializing in information technology, the administrator decided to draw 3 different qualification courses among its 10 employees. Considering that the same employee cannot be drawn more than once, the total number of different ways of drawing among employees is:

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Answer to a math question To celebrate the five-year anniversary of a consultancy specializing in information technology, the administrator decided to draw 3 different qualification courses among its 10 employees. Considering that the same employee cannot be drawn more than once, the total number of different ways of drawing among employees is:

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Neal
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54 Answers
Para encontrar o número total de maneiras diferentes de sortear 3 cursos distintos entre 10 funcionários, podemos usar o conceito de combinação.

A fórmula para calcular a combinação de n elementos tomados de k em k é dada por:

C(n,k) = \frac{n!}{k!(n-k)!}

Onde "n!" representa o fatorial de n.

Aplicando essa fórmula ao nosso problema, temos:

C(10,3) = \frac{10!}{3!(10-3)!}

Simplificando a expressão:

C(10,3) = \frac{10!}{3!7!}

Calculando os fatoriais:

C(10,3) = \frac{10 \times 9 \times 8 \times 7!}{3! \times 7!}
C(10,3) = \frac{10 \times 9 \times 8}{3 \times 2 \times 1}
C(10,3) = 120

Portanto, o total de maneiras diferentes de sortear 3 cursos distintos entre os 10 funcionários é igual a 120.

\textbf{Resposta:} O total de maneiras diferentes de sortear 3 cursos distintos entre os funcionários é 120.

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