A die is rolled 10 times.find th no. of ways so that outcomes always contain 1,2,3.

I cannot understand how to approach the solution.someone pls help.

THANKING YOU

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- April 5th 2009, 02:48 AMananya janaPermutation & combination problem
A die is rolled 10 times.find th no. of ways so that outcomes always contain 1,2,3.

I cannot understand how to approach the solution.someone pls help.

THANKING YOU - April 5th 2009, 03:36 AMPlato
- April 5th 2009, 03:55 AMSoroban
Hello, ananya jana!

I'll take aat what the question asks . . .*guess*

Quote:

A die is rolled 10 times.

Find the number of ways so that outcomes always contain a 1, 2, or 3.

With a sequence of 10 rolls, there are: . possible outcomes.

How many of these rolls contain**no**1s, 2s, or 3s?

The rolls must consist of 4, 5, and/or 6 only.

. . There are: . ways.

Therefore, there are: . ways.

- April 5th 2009, 04:13 AMananya jana
- April 5th 2009, 04:16 AMananya jana
but we cannot count the outcome where 1 4 5 6 4 5 4 5 6 1

because 2 and 3 are absent...

but this outcome may come in the

outcomes - April 5th 2009, 06:52 AMSoroban
Hello again, ananya jana!

See? . . . You have a different interpretation of the problem!

If that was the exact wording, the problem is poorly written.

Quote:

A die is rolled 10 times.

Find the number of ways so that the outcomes

always contain*at least*one 1, one 2,**and**one 3.

There are: . possible outcomes.

Let: .

. .

. .

. .

Formula: .

. .

. .

There are 26,210,196 outcomes with no 1**or**no 2**or**no 3.

Therefore, there are: . outcomes

. . that contain at least one 1, one 2, and one 3.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Another interpretation . . .

Number of outcomes that contain**exactly**one 1, one 2, and one 3.

The 1,2,3 can occur in any of: . sequences of rolls.

The other seven rolls mustbe 1, 2, or 3: . ways.__not__

Therefore, there are: . ways.