Question

there are 5 different roads from city a to city b.Three different roads from b to c and four different road that go directly from a to c.how many ways are there from a to c altogether

Answer 1

Answer:

If there are four roads from city A to city B, three roads from city B to city C, and two roads from city C to city D, how many ways are there to go and come back from A to D via B and C if a road cannot be used more than once?

Initially from A to D through B and C

We have = 4 x 3 x 2 = 24 ways

While returning from D to A through B and C we cannot choose the previous paths

So from D to C instead of 2 ways we have one

From C to B instead of 3 ways we have 2

And from B to A instead of 4 we have 3 ways

So number of ways we have from D to A will be = (4–1) x (3–1) x (2–1) = 3x2x1 = 6

Now total round trip ways become = 24 x 6 = 144

Taking example of above image we have

From A to D the following ways

aeh, aei, afh, afi, agh, agi

beh, bei, bfh, bfi, bgh, bgi

ceh, cei, cfh, cfi, cgh, cgi

deh, dei, dfh, dfi, dgh, dgi. (24)

Now suppose we t

There are 3 different roads going from town A to town B, 4 different roads from town B to C and 3 different roads from town C to town D. How many different options do you have when travelling from town A to town D?

If there are 3 roads from town A to town B, and 4 roads from town B to town C, in how many ways can one go from town A to town C and back to town A trough town B without passing trough the same road twice?

There are 3 different roads from city A to city B and 2 different roads from city B to city C. In how many ways can someone go from city A to city C passing by city B?

A postman can travel from village A to B by four different roads, from village B to C by two different roads and from village C to village D by 3different roads. If the postman goes from village A to village D and comes back by a different route, in how many ways can he do this?

There are 4 cities situated at the end points of a square with sides of 10km. What is the minimum length of the road such that we can go from one city to another?

The answer is 144! .

When you are going to C to D there are 2 ways.

B to C 3 ways then

There are 3 ways

So you can use 3*2= 6

Ways to go B to D

Like wise that you can use 4*3*2= 24

Ways.

4! = 24

Then returning

There are 3 ways you can use B to A

2 ways C to B

One way D to C

Then back you can use 3*2*1 = 6 = 3!

So all you can use 24*6 = 144 ways.