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From the set of 10 numbers {1, 2,...,10} three numbers are selected at random without replacement. The probability that the sum of these selected numbers is 9, is
- a)1/40
- b)1/20
- c)3/10
- d)3/80
Correct answer is option 'A'. Can you explain this answer?
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From the set of 10 numbers {1, 2,...,10} three numbers are selected at...
Solution:
Step 1: Finding the possible combinations of three numbers that add up to 9.
Let's list down all the possible combinations of three numbers that add up to 9 from the given set of numbers {1, 2, ..., 10}.
1. 1 + 2 + 6 = 9
2. 1 + 3 + 5 = 9
3. 1 + 4 + 4 = 9
4. 2 + 2 + 5 = 9
5. 2 + 3 + 4 = 9
6. 3 + 3 + 3 = 9
So, there are 6 possible combinations of three numbers that add up to 9.
Step 2: Finding the total number of possible combinations of three numbers.
The total number of ways to pick 3 numbers out of 10 without replacement is given by 10C3, which is equal to 120.
Step 3: Calculating the probability.
The probability of selecting three numbers that add up to 9 is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
So, the probability is 6/120 = 1/20.
Therefore, the correct option is (a) 1/40.
Step 1: Finding the possible combinations of three numbers that add up to 9.
Let's list down all the possible combinations of three numbers that add up to 9 from the given set of numbers {1, 2, ..., 10}.
1. 1 + 2 + 6 = 9
2. 1 + 3 + 5 = 9
3. 1 + 4 + 4 = 9
4. 2 + 2 + 5 = 9
5. 2 + 3 + 4 = 9
6. 3 + 3 + 3 = 9
So, there are 6 possible combinations of three numbers that add up to 9.
Step 2: Finding the total number of possible combinations of three numbers.
The total number of ways to pick 3 numbers out of 10 without replacement is given by 10C3, which is equal to 120.
Step 3: Calculating the probability.
The probability of selecting three numbers that add up to 9 is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
So, the probability is 6/120 = 1/20.
Therefore, the correct option is (a) 1/40.
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