Find the probability that getting 4 digit number with 1 in the unit pl

1.	Find the probability that getting 4 digit number with 1 in the unit place and 2 in the tens place when the numbers 1,2,3,4 and 5 are arranged at random without repeating.
Answer» 1/20 The numbers can be WRITTEN in 5! different ways then n(S) = 5! = 120 Let E be the EVENT that getting 4 DIGIT NUMBER with 1 in the unit place and 2 in the tens place when the numbers 1,2,3,4 and 5 are arranged at random. Since each desired number is ending with 1,there is only 1 way. The Second place(tens) can now be filled with 2. Here also only 1 way to fill. The next place(hundreds) can now be filled by any of the remaining 3 numbers. So, there are 3 ways to filling that place. Then, the first place can now be filled by any of the remaining 2 numbers. So, there are 2 ways to fill. Therefore n(E) = 1 x 1 x 3 x 2 = 6. Now, p(E) = n(E) / n(S) = 6 / 120 = 1/20. Hence the required probability is 1/20.

Find the probability that getting 4 digit number with 1 in the unit place and 2 in the tens place when the numbers 1,2,3,4 and 5 are arranged at random without repeating.

Answer»

1/20

The numbers can be WRITTEN in 5! different ways then n(S) = 5! = 120
Let E be the EVENT that getting 4 DIGIT NUMBER with 1 in the unit place and 2 in the tens place when the numbers 1,2,3,4 and 5 are arranged at random.
Since each desired number is ending with 1,there is only 1 way.
The Second place(tens) can now be filled with 2.
Here also only 1 way to fill.
The next place(hundreds) can now be filled by any of the remaining 3 numbers.
So, there are 3 ways to filling that place.
Then, the first place can now be filled by any of the remaining 2 numbers.
So, there are 2 ways to fill.
Therefore n(E) = 1 x 1 x 3 x 2 = 6.
Now, p(E) = n(E) / n(S) = 6 / 120 = 1/20.
Hence the required probability is 1/20.

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