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rosijanka [135]
3 years ago
13

A standard six-sided die is rolled $6$ times. You are told that among the rolls, there was one $1,$ two $2$'s, and three $3$'s.

How many possible sequences of rolls could there have been? (For example, $3,2,3,1,3,2$ is one possible sequence.)
Mathematics
1 answer:
Alex777 [14]3 years ago
7 0

Answer:

Sequence = 120

Step-by-step explanation:

Given

6 rolls of a die;

Required

Determine the possible sequence of rolls

From the question, we understand that there were three possible outcomes when the die was rolled;

The outcomes are either of the following faces: 1, 2 and 3

Total Number of rolls = 6

Possible number of outcomes = 3

The possible sequence of rolls is then calculated by dividing the factorial of the above parameters as follows;

Sequence = \frac{6!}{3!}

Sequence = \frac{6 * 5 * 4* 3!}{3!}

Sequence = 6 * 5 * 4

Sequence = 120

Hence, there are 120 possible sequence.

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The ratio of the cost of a shirt to the cost of a jacket is 2:5. If the jacket cost $240 more than the shirt,
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Given:

The ratio of the cost of a shirt to the cost of a jacket is 2:5.

The jacket cost $240 more than the shirt.

To find:

The cost of the shirt and the cost of the jacket.

Solution:

Let x be the cost of the shirt.

The jacket cost $240 more than the shirt. So, the cost of Jacket is (x+240).

The ratio of the cost of a shirt to the cost of a jacket is 2:5. So,

\dfrac{x}{x+240}=\dfrac{2}{5}

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Subtract 2x from both sides.

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Divide both sides by 3.

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So, the cost of shirt is $160.

Now, the cost of jacket is:

160+240=400

Therefore, the cost of shirt is $160 and the cost of jacket is $400.

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