1. ## Arrangements

Dear All,

I have few questions on probability, that's

1) sunitha wants to make a necklace. she has 8 beads how many different choices does she have?
2)from city A to B there are 3 different roads, from B to C there are 5, from C to D there are 2.Laxman has to go from city A to D attending some work in city B and C on the way and has to come back in the reverse order.In how many ways can he complete his journey if he has to take a different while coming back than he did while going?

2. Originally Posted by vijayayarra
1) sunitha wants to make a necklace. she has 8 beads how many different choices does she have?
Only one if all the beads are alike.

3. Hello, vijayayarra!

Both problems are poorly worded.
I must make some guesses . . .

1) Sunitha wants to make a necklace. She has 8 beads.
How any different choices does she have?

I will assume that there are 8 distinguishable beads,
. . perhaps of 8 different colors.
I will also assume that her necklace will have all 8 beads,
. . and that the question is: "How many different necklaces can be made?"

Placing 8 items in a circle, there are: . $7!$ ways.

But half of them are mirror-images of the other half.

Therefore, there are: . $\frac{7!}{2} \:=\:2520$ possible necklaces.

2) From city A to B there are 3 different roads,
from B to C there are 5, and from C to D there are 2.
Laxman has to go from city A to D attending some work
in cities B and C on the way and has to come back in the reverse order.

In how many ways can he complete his journey if he has to
take a different route while coming back than he did while going?

Going from A to D, there are: . $3 \times 5 \times 2 \:=\:30$ choices.

Now what is meant by "a different route"?

If it means that no road can be used more than once,
then on the return trip, there are:
. . 1 choice for D-to-C,
. . 4 choices for C-to-B,
. . 2 choices for B-to-A.

Hence, there are: . $1 \times 4 \times 2 \:=\:8$ choices for the return trip.

If "a different route" means even slightly different, then the trip from D to A
. . must not be exactly the same as the route from A to D.
Then there are: . $30 - 1 \:=\:29$ choices for the return trip.

4. ## circular probability

Hello,

1) sunitha wants to make a necklace. she has 8 beads how many different choices does she have?
Ans. 1200
2)from city A to B there are 3 different roads, from B to C there are 5, from C to D there are 2.Laxman has to go from city A to D attending some work in city B and C on the way and has to come back in the reverse order.In how many ways can he complete his journey if he has to take a different while coming back than he did while going?
Ans.870

Sorry above ones are the correct answers but I don't understand the logic behind that.

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# sunita wants to make a necklace

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