Hello, sous!

There are: . possible outcomes.8. A and B each throw a set of three dice.

If A throws a total of 16, B’s probability of getting a higher total is:

. .

To get a higher total, must get a 17 or 18.

There are only 4 such outcomes: .

Therefore: .

Let: . - vowel, . = consonant.9. If all the letters of the word ‘TRIANGLE’ are taken and permuted in all ways,

then the number of arrangements in which the relative positions of vowels and consonants remain unaltered is:

. .

The permutation has the form: .

The consonants can be placed in: . ways.

The vowels can be placed in: . ways.

Therefore, there are: . permutations.

Since there are 28 connecting roads, there must be#10 has a typo.

I'll take aat what was meant.guess

10. The cities A, B, C, D, E, F, G, H are located so they form the vertices of a regular polygon.

Each city is connected to every other city by means of the shortest possible highway.

The total number of highways connecting the cities is 28.

What is the total number of ways in which a person can travel from the city A to city C,

provided that during his travel he visits no city more than once?

. .8cities.

I found no neat formula for this problem . . . I had to make a list.

One-step tour

He drives directly from to : .1 way.

Two-step tour

He drives from to one of the other 6 cities,

. . then drives to : . ways.

Three-step tour

He drives from through two of the other 6 cities (in some order)

. . then drives to : . ways.

Four-step tour

He drives from through three of the other 6 cities (in some order)

. . then drives to : . ways.

Five-step tour

He drives from through four of the other 6 cities (in some order)

. . then drives to : . ways.

Six-step tour

He drives from through five of the other 6 cities (in some order)

. . then drives to : . ways.

Seven-step tour

He drives from through all six of the other 6 cities (in some order)

. . then drives to : . ways.

Therefore, there are: . ways.