All questions of Probability for SSC CGL Exam

Understanding the Problem
To find out how many 3-digit numbers can be formed using the digits 1, 3, 5, 6, and 8 with repetition allowed, we need to analyze the choices available for each digit in the number.
Available Digits
The digits we can use are:
- 1
- 3
- 5
- 6
- 8
This gives us a total of 5 different digits.
Forming a 3-Digit Number
A 3-digit number has three positions: the hundreds place, the tens place, and the units place.
- Hundreds Place: We can choose any of the 5 digits.
- Tens Place: Again, we can choose any of the 5 digits.
- Units Place: Similarly, we can choose any of the 5 digits.
Calculating Total Combinations
Since repetition is allowed, the number of choices for each position is independent of the others. Therefore, we can calculate the total combinations as follows:
- Choices for Hundreds Place: 5
- Choices for Tens Place: 5
- Choices for Units Place: 5
Final Calculation
To find the total number of 3-digit combinations:
- Total Combinations = Choices for Hundreds × Choices for Tens × Choices for Units
= 5 × 5 × 5 = 125
Thus, the total number of 3-digit numbers that can be formed is 125.
Conclusion
The correct answer to the problem is option 'D' (125). This method can be applied to similar problems involving combinations and repetitions.

Understanding the Problem
To determine how many 4-digit numbers can be formed using the digits 2, 3, 4, and 5 with repetition allowed, we follow a systematic approach.
Available Digits
- The digits available are: 2, 3, 4, 5.
- This gives us a total of 4 digits to choose from.
Number of Positions
- We need to form a 4-digit number.
- There are 4 positions to fill: thousands, hundreds, tens, and units.
Choosing Digits for Each Position
- Since repetition is allowed, each of the 4 positions can be filled with any of the 4 digits.
- Thus, for each position, we have 4 choices.
Calculating the Total Combinations
- The total number of combinations can be calculated using the formula:
Total combinations = (Number of choices for the first position) x (Number of choices for the second position) x (Number of choices for the third position) x (Number of choices for the fourth position)
- In this scenario:
Total combinations = 4 (for the first position) x 4 (for the second position) x 4 (for the third position) x 4 (for the fourth position)
- This simplifies to:
4 x 4 x 4 x 4 = 4^4
- Evaluating this gives:
4^4 = 256.
Final Answer
- Therefore, the total number of 4-digit numbers that can be formed is 256, which corresponds to option 'D'.

Isn't 1divisible by 3

Understanding the Problem
In a bag, there are:
- 6 black balls
- 5 red balls
Total balls = 6 + 5 = 11 balls.
We want to find the probability of choosing 3 black balls when 3 balls are drawn at random.
Calculating Total Ways to Choose Balls
The total number of ways to choose 3 balls from 11 is calculated using the combination formula:
- Total combinations = C(11, 3)
Calculating the Combinations
- C(11, 3) = 11! / (3!(11-3)!) = 165
Calculating Ways to Choose Black Balls
Next, we calculate the number of ways to choose 3 black balls from the 6 available:
- Combinations for black balls = C(6, 3)
Calculating Black Ball Combinations
- C(6, 3) = 6! / (3!(6-3)!) = 20
Finding the Probability
Now, the probability that all 3 chosen balls are black is given by the ratio of the number of favorable outcomes to the total outcomes:
- Probability = (Number of ways to choose 3 black balls) / (Total ways to choose 3 balls)
- Probability = C(6, 3) / C(11, 3) = 20 / 165 = 4 / 33
Conclusion
The probability that all three balls chosen are black is:
- Option B: 4/33

Understanding the Problem
To find the number of ways to rearrange the letters of the word "DEER," we need to account for the repetitions of the letters. The word consists of four letters: D, E, E, and R.
Identifying Letter Frequencies
- Total letters: 4
- Frequency of D: 1
- Frequency of E: 2
- Frequency of R: 1
Applying the Formula for Permutations of Multisets
The formula to calculate the permutations of a multiset is given by:
Total permutations = n! / (p1! * p2! * ... * pk!)
Where:
- n = total number of items
- p1, p2, ... pk = frequencies of each unique item
For the word "DEER":
- n = 4 (total letters)
- p1 = 1 (for D)
- p2 = 2 (for E)
- p3 = 1 (for R)
Thus, the calculation becomes:
Total permutations = 4! / (1! * 2! * 1!)
Calculating Factorials
- 4! = 4 × 3 × 2 × 1 = 24
- 1! = 1
- 2! = 2 × 1 = 2
Now substitute into the formula:
Total permutations = 24 / (1 * 2 * 1) = 24 / 2 = 12
Final Conclusion
The number of distinct arrangements of the letters in "DEER" is 12. Therefore, the correct answer is option 'D': None of these.