There are $5$ red, $4$ white and $3$ blue marbles in a bag. They are drawn one by one and arranged in a row. Assuming that the $12$ marbles are drawn, determine the number of different arrangements.

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Solution

Using the formula for arrangements of $n$ objects of which there might be groups of indistinguishable objects.

In this example, $12$ marbles, consisting of indistinguishable groups of $4$ white, $5$ red, and $3$ blue marbles.

Number of ways $= \frac{12!}{5! \times 4! \times 3!} = 27720$

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There are 5 red, 4 white and 3 blue marbles in a bag. They are drawn one by one and arranged in a row. Assuming that the 12 marbles are drawn, determine the number of different arrangements.

Using the formula for arrangements of n objects of which there might be groups of indistinguishable objects. In this example, 12 marbles, consisting of indistinguishable groups of 4 white, 5 red, and 3 blue marbles.Number of ways =12!5!×4!×3!=27720

There are $5$ red, $4$ white and $3$ blue marbles in a bag. They are drawn one by one and arranged in a row. Assuming that the $12$ marbles are drawn, determine the number of different arrangements.

Using the formula for arrangements of $n$ objects of which there might be groups of indistinguishable objects.

In this example, $12$ marbles, consisting of indistinguishable groups of $4$ white, $5$ red, and $3$ blue marbles.

Number of ways $= \frac{12!}{5! \times 4! \times 3!} = 27720$