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MrRa [10]
3 years ago
11

kangaroo wants to arrange the twelve numbers from 1 to 12 in a circle in such a way that any neighboring numbers always differ b

y either 1 or 2 which of the following pairs of numbers have to be neighbors
Mathematics
1 answer:
Deffense [45]3 years ago
3 0
Start by laying out the 12.
The neighbors of 12 must be 11 and 10.
The neighbor of 11 must be 9, and the neighbor of 10 must be 8, and so on and so forth, until you get a unique arrangement.

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Katarina [22]

Answer:

\dfrac{5}{6}

Step-by-step explanation:

When two dice are rolled, the sample space is

\begin{array}{cccccc}(1,1)&(1,2)&(1,3)&(1,4)&(1,5)&(1,6)\\(2,1)&(2,2)&(2,3)&(2,4)&(2,5)&(2,6)\\(3,1)&(3,2)&(3,3)&(3,4)&(3,5)&(3,6)\\(4,1)&(4,2)&(4,3)&(4,4)&(4,5)&(4,6)\\(5,1)&(5,2)&(5,3)&(5,4)&(5,5)&(5,6)\\(6,1)&(6,2)&(6,3)&(6,4)&(6,5)&(6,6)\end{array}

In total, 36 outcomes

First, find the probability that the sum is 10 or greater:

All favorable outcomes

10: (4,6),\ (5,5),\ (6,4)

11: (5,6),\ (6,5)

12: (6,6)

In total, 6 outcomes.

The probability that the sum is 10 or greater is

P(A)=\dfrac{6}{36}=\dfrac{1}{6}

Use the complement rule to find that the probability that the sum of the dice is less than 10:

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