Permutation And Combination Questions MCQs


permutation and combination Questions

Total Questions : 102

Page 1 of 6 pages
Question 1. Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side.
  1.    864
  2.    863
  3.    865
  4.    1728
Answer: Option D
Question 2. A man positioned at the origin of the coordinate system. the man can take steps of unit measure in the direction North, East, West or South. Find the number of ways of he can reach the point (5,6), covering the shortest possible distance.
  1.    252
  2.    432
  3.    462
  4.    504
Answer: Option C
Question 3. There are 2 brothers among a group of 20 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers?
  1.    2 × 17!
  2.    18! × 18
  3.    19! × 18
  4.    2 × 18!
  5.    2 × 17! × 17!
Answer: Option D
Question 4. There are 6 equally spaced points A, B, C, D, E and F marked on a circle with radius R. How many convex pentagons of distinctly different areas can be drawn using these points as vertices?
  1.    6P5
  2.    1
  3.    5
  4.    None of these
Answer: Option D
Question 5. A, b, c, d and e are five natural numbers. Find the number of ordered sets (a, b, c, d, e) possible such that a + b + c + d + e = 64.
  1.    64C5
  2.    63C4
  3.    65C4
  4.    63C5
Answer: Option B
Question 6. There are five cards lying on the table in one row. Five numbers from among 1 to 100 have to be written on them, one number per card, such that the difference between the numbers on any two adjacent cards is not divisible by 4. The remainder when each of the 5 numbers is divided by 4 is written down on another card (the 6th card) in order. How many sequences can be written down on the 6th card?
  1.    210
  2.    210 × 33
  3.    4 × 34
  4.    42 × 33
Answer: Option C
Question 7. From a total of six men and four ladies a committee of three is to be formed. If Mrs. X is not willing to join the committee in which Mr. Y is a member, whereas Mr.Y is willing to join the committee only if Mrs Z is included, how many such committee are possible?
  1.    138
  2.    128
  3.    112
  4.    91
Answer: Option D
Question 8. Goldenrod and No Hope are in a horse race with 6 contestants. How many different arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?
  1.    700
  2.    360
  3.    120
  4.    24
  5.    21
Answer: Option B
Question 9. How many words of 4 consonants and 3 vowels can be made from 12 consonants and 4 vowels, if all the letters are different?
  1.    16C7 × 7!
  2.    12C4 × 4C3 × 7!
  3.    12C3 × 4C4
  4.    11C4 × 4C3
Answer: Option B
Question 10. Jay wants to buy a total of 100 plants using exactly a sum of Rs. 1000. He can buy Rose plants at Rs. 20 per plant or marigold or Sun flower plants at Rs. 5 and Rs. 1 per plant respectively. If he has to buy at least one of each plant and cannot buy any other type of plants, then in how many distinct ways can Jay make his purchase?
  1.    2
  2.    3
  3.    4
  4.    5
  5.    None of these
Answer: Option B
Question 11. A local delivery company has three packages to deliver to three different homes. if the packages are delivered at random to the three houses, how many ways are there for at least one house to get the wrong package?
  1.    3
  2.    5
  3.    3!
  4.    5!
Answer: Option B
Question 12. In how many ways can a leap year have 53 Sundays?
  1.    365C7
  2.    7
  3.    4
  4.    2
Answer: Option D
Question 13. How many natural numbers less than a lakh can be formed with the digits 0,6 and 9?
  1.    242
  2.    243
  3.    728
  4.    729
Answer: Option A
Question 14. There are 20 couples in a party. Every person greets every person except his or her spouse. People of the same sex shake hands and those of opposite sex greet each other with a Namaste (It means bringing one's own palms together and raising them to the chest level). What is the total number of handshakes and Namaste's in the party?
  1.    760
  2.    1140
  3.    780
  4.    720
Answer: Option B
Question 15. In a certain laboratory, chemicals are identified by a colour-coding system. There are 20 different chemicals. Each one is coded with either a single colour or a unique two-colour pair. If the order of colours in the pairs does not matter, what is the minimum number of different colours needed to code all 20 chemicals with either a single colour or a unique pair of colours?
  1.    7
  2.    6
  3.    5
  4.    8
Answer: Option B
Question 16. Six boxes are numbered 1, 2, 3, 4, 5 and 6. Each box must contain either a white ball or a black ball. At least one box must contain a black ball and boxes containing black balls must be consecutively numbered. find the total number of ways of placing the balls.
  1.    15
  2.    20
  3.    21
  4.    36
Answer: Option C
Question 17. In how many ways can 6 green toys and 6 red toys be arranged, such that 2 particular red toys are never together whereas 2 particular green toys are always together?
  1.    11! × 2!
  2.    9! × 90
  3.    4 × 10!
  4.    18 × 10!
Answer: Option D
Question 18. There are five comics numbered from 1 to 5. In how many ways can they be arranged, so that part-1 and part-3 are never together?
  1.    48
  2.    72
  3.    120
  4.    210
Answer: Option B
Question 19. Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
  1.    210
  2.    29
  3.    3 × 28
  4.    None of these
Answer: Option B
Question 20. The number of ways which a mixed double tennis game can be arranged amongst 9 married couples if no husband and wife play in the same is:
  1.    1514
  2.    1512
  3.    3024
  4.    3028
Answer: Option B