PIEAS Entry Test Mathematics Permutation & Combination — Set 2

Permutation & Combination MCQs set 2 for PIEAS Entry Test Mathematics — 20 solved questions.

PIEAS Entry Test Mathematics Permutation & Combination — Set 2

  1. Question 1

    Q1. A committee of 5 is to be formed from 6 men and 4 women. How many ways can this be done if it must contain at least 2 women?

    • A) 180
    • B) 186
    • C) 210
    • D) 216

    Answer: 186

    Explanation: Using combination formula, C(4,2)*C(6,3) + C(4,3)*C(6,2) + C(4,4)*C(6,1) = 186. Applying principle of inclusion.

  2. Question 2

    Q2. What is the probability that a randomly chosen 3-digit number is divisible by 3?

    • A) 1 / 3
    • B) 1 / 2
    • C) 1 / 4
    • D) 3 / 10

    Answer: 1 / 3

    Explanation: Using divisibility rule, 1/3 numbers are divisible by 3. Hence, probability = 1 / 3.

  3. Question 3

    Q3. If P(A) = 0.4, P(B) = 0.5 and P(A ∩ B) = 0.2, then P(A|B) is

    • A) 0.4
    • B) 0.5
    • C) 0.6
    • D) 0.8

    Answer: 0.4

    Explanation: P(A|B) = P(A ∩ B) / P(B) = 0.2 / 0.5 = 0.4. Using conditional probability formula.

  4. Question 4

    Q4. A bag contains 5 red and 3 black balls. What is the probability that 2 balls drawn are of different colors?

    • A) 15 / 28
    • B) 13 / 28
    • C) 15 / 56
    • D) 13 / 56

    Answer: 15 / 28

    Explanation: P(different colors) = (C(5,1)*C(3,1)) / C(8,2) = 15 / 28. Using combination and probability formula.

  5. Question 5

    Q5. How many 4-digit numbers can be formed using digits 1, 2, 3, 4, 5 without repetition?

    • A) 120
    • B) 60
    • C) 24
    • D) 1200

    Answer: 120

    Explanation: Using permutation formula for 5 digits taken 4 at a time, P(5,4) = 5! / (5-4)! = 120.

  6. Question 6

    Q6. In how many ways can 5 boys and 3 girls be seated in a row so that no two girls are together?

    • A) 14400
    • B) 1440
    • C) 7200
    • D) 720

    Answer: 14400

    Explanation: First arranging 5 boys in 5! ways, then 3 girls in 6P3 ways. So, total = 5! * 6P3 = 14400.

  7. Question 7

    Q7. A number is chosen at random from the first 100 natural numbers. What is the probability that it is divisible by 4 or 6?

    • A) 41 / 100
    • B) 33 / 100
    • C) 1 / 3
    • D) 1 / 2

    Answer: 41 / 100

    Explanation: Count numbers divisible by 4 or 6, then divide by 100. Using principle of inclusion-exclusion.

  8. Question 8

    Q8. How many different 5-letter words can be formed using the letters of 'DELHI'?

    • A) 60
    • B) 120
    • C) 24
    • D) 5

    Answer: 120

    Explanation: Using permutation formula for 5 distinct letters, 5! = 120.

  9. Question 9

    Q9. If P(A ∪ B) = 0.8, P(A) = 0.3, P(B) = 0.5, then P(A ∩ B) is

    • A) 0
    • B) 0.1
    • C) 0.2
    • D) 0.3

    Answer: 0.2

    Explanation: Using formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B), we get P(A ∩ B) = 0.3 + 0.5 - 0.8 = 0.

  10. Question 10

    Q10. In a box, there are 5 red, 4 blue, and 3 green balls. What is the probability of drawing a red ball first and then a blue ball?

    • A) 5 / 33
    • B) 5 / 12
    • C) 20 / 132
    • D) 1 / 6

    Answer: 5 / 33

    Explanation: P(red then blue) = P(red) * P(blue) = (5/12) * (4/11) = 5 / 33. Using multiplication rule.

  11. Question 11

    Q11. A die is thrown. What is the probability of getting a number greater than 4?

    • A) 1 / 3
    • B) 2 / 3
    • C) 1 / 2
    • D) 1 / 6

    Answer: 1 / 3

    Explanation: Numbers greater than 4 on a die are 5 and 6, so probability is 2/6 = 1/3.

  12. Question 12

    Q12. How many ways can the letters of 'BANANA' be arranged?

    • A) 60
    • B) 120
    • C) 720
    • D) 360

    Answer: 60

    Explanation: Using formula for permutations with repetitions, 6! / (3! * 2!) = 60.

  13. Question 13

    Q13. The probability of A hitting a target is 1/3 and that of B is 1/5. If they fire together, what is the probability that the target is hit?

    • A) 7 / 15
    • B) 8 / 15
    • C) 2 / 3
    • D) 1 / 3

    Answer: 7 / 15

    Explanation: P(at least one hits) = 1 - P(neither hits) = 1 - (2/3)*(4/5) = 7/15. Using complementary probability.

  14. Question 14

    Q14. In a lottery, there are 10 prizes and 25 blanks. What is the probability of getting a prize?

    • A) 2 / 7
    • B) 2 / 5
    • C) 1 / 3
    • D) 1 / 5

    Answer: 2 / 7

    Explanation: P(prize) = Number of prizes / Total outcomes = 10 / (10 + 25) = 2 / 7.

  15. Question 15

    Q15. A committee of 3 is to be formed from 4 men and 5 women. What is the probability that it contains at least 2 women?

    • A) 17 / 21
    • B) 5 / 7
    • C) 10 / 21
    • D) 15 / 21

    Answer: 17 / 21

    Explanation: P(at least 2 women) = (C(5,2)*C(4,1) + C(5,3)) / C(9,3) = 17 / 21. Using combination and probability.

  16. Question 16

    Q16. Two dice are thrown. What is the probability that the sum is 7?

    • A) 1 / 6
    • B) 1 / 12
    • C) 1 / 9
    • D) 1 / 36

    Answer: 1 / 6

    Explanation: P(sum = 7) = Number of favorable outcomes / Total outcomes = 6 / 36 = 1 / 6.

  17. Question 17

    Q17. A bag contains 4 red and 6 black balls. A ball is drawn at random. What is the probability that it is red?

    • A) 2 / 5
    • B) 3 / 5
    • C) 2 / 3
    • D) 1 / 5

    Answer: 2 / 5

    Explanation: P(red) = Number of red balls / Total balls = 4 / 10 = 2 / 5.

  18. Question 18

    Q18. A bag contains 5 red and 3 blue balls. What is the probability of drawing a blue ball?

    • A) 3 / 8
    • B) 1 / 2
    • C) 3 / 5
    • D) 1 / 4

    Answer: 3 / 8

    Explanation: Total balls = 8, blue balls = 3. Probability = Number of blue balls / Total balls = 3 / 8

  19. Question 19

    Q19. How many ways can 3 prizes be given to 5 students if a student can receive more than one prize?

    • A) 125
    • B) 60
    • C) 120
    • D) 15

    Answer: 125

    Explanation: For each prize, 5 choices. Total = 5 * 5 * 5 = 125

  20. Question 20

    Q20. What is the probability that a randomly chosen number between 1 and 100 is divisible by 5?

    • A) 1 / 5
    • B) 1 / 10
    • C) 1 / 4
    • D) 1 / 20

    Answer: 1 / 5

    Explanation: Numbers divisible by 5 = 20. Total numbers = 100. Probability = 20 / 100 = 1 / 5