Permutation and Combination Problems with Solutions for IBPS Exam
Permutation and Combination Problems with Solutions with solution for SSC Exam
Permutation Permutation is the total number of different ways of arrangements
Number of ways of arrangements of n different things = n!
For example In how many different ways can the letters of word ‘TIGER’ be arranged
Solution Since there are five different letters, so total arrangements = 5! = 120
But if the letters or numbers are repeating suppose there are n numbers out of which two numbers are repeated 2 times and 3 times respectively. Then total arrangements = n! / (2!×3!)
For example Total arrangements of the letters of the word ‘committee’ is equal to
9! /( 2!×2!× 2!) = 45360
Number of ways of arrangements of r things taken at a time out of n different things = nPr
nPr = n! / (n-r)!
For example How many three digits number can be formed with the digits 1,2,3,4,5,6, if repetition of digits is not allowed
Solution 6P3 = 6 ! / (6 – 3) ! = 6! / 3! = 720 / 6 = 120
Combination Combination is the total number of ways of selecting or choosing total number of ways of selecting r things taken at a time out of n different things = nCr
nCr = n! / [r! (n – r)!]
For example In how many different ways can we choose 4 persons out of 6 persons
Solution 6C4 = 6! / 4! (6 – 4)! = 6! / (4! 2!) = 6*5*4*3*2*1 / 4*3*2*1*2*1 = 6*5 / 2 = 15
Total number of different ways of arrangements of n persons around a circular table = ( n – 1 )!
In permutation and combination ‘or’ means +, ‘and’ means
Suppose we have to form a group of 3 men and 1 women out of 5 men and 4 women
Total number of ways of forming this group = 5C3 and 4C1
= 5C3 × 4C1 = 10*4 = 40
Now suppose we have to form a group of 2 people of same gender ( i.e. both men or both women) out of 5 men and 4 women
Total number of ways = 5C2 or 4C2
= 5C3 + 4C2 = 10 + 6 = 16
Experiment : An activity which results in some well defined outcomes is called an experiment.
Random Experiment : An experiment whose outcomes cannot be predicted is called random experiment
Here are some examples of random experiment
Tossing of a coin If we toss a coin either a head or tail will come up. But we cannot predict with certainty out of head or tail before our results
Drawing a card from a well shuffled pack of 52 playing cards
Throwing an unbiased dice If we throw a dice then the possible outcomes are 1, 2, 3, 4, 5, 6
Information about playing cards
There are total of 52 cards
Types number of cards color
Spade 13 cards black
Heart 13 cards red
Club 13 cards black
Diamond 13 cards red
2,3,4,5,6,7,8,9,10, Jack , Queen, King and Ace are the thirteen cards of each type
Probability The probability of any event E is calculated as favorable event divided by the total event
P (E) = favorable event / total event
Practice set problems
1. Find the total arrangements of the letters of word ‘ MISSISSIPPI ‘
a. 34650 b. 32540 c. 28450 d. 24560 e. None of these
2. Out of 5 men and 3 women, a committee of 3 members is to be formed so that it has 1 woman and 2 men. In how many different ways can it be done ?
a.20 b. 10 c.23 d. 30 e. None of these
United Bank Of India PO Exam. 21.06.2009
3. In how many different ways can the letters of the word DESIGN be arranged so that the vowels are at the two ends ?
a. 48 b. 72 c. 36 d.24 e. None of these
United Bank Of India PO Exam. 21.06.2009
4. In how many different ways can the letters of the word PUNCTUAL be arranged ?
a.64 b. 40320 c. 960 d. 20160 e. None of these
SBI PO Preliminary exam. 27.07.200
5. In how many different ways can the letters of the word CORPORATION be arranged in such a way that the vowels always come together ?
a.840 b. 86400 c. 8400 d. 1440 e. None of these
SBI BANKS PO EXAM. 18.05.2003
6. A committee of five members is to be formed out of 4 students, 3 teachers and 2 sports coaches. In how many can the committee be formed such that the committee should consist of any five people ?
a. 126 b.45 c. 120 d. 24 e. None of these
United Bank Of India PO Exam. 14.11.2010
7. Find the total arrangements of the letters of the word ‘INVISIBILITY’ such that all I always come together
a. 7! × 5! b. 8! c.8! × 5! d. 7! e. none of these
8. A group of 7 persons is to be formed from 6 men and 8 women such that the men are in majority. In how many ways this can be done ?
a. 780 b. 1260 c. 1016 d. Cannot be determined e. None of these
9. How many 7_ digits numbers can be formed using the digits 1,2,3,4,5,0,6 such that unit place is 6 and repetition of digits is not allowed ?
a.720 b. 600 c. 120 d. 7! e. None of these
10. How many even numbers can be formed using the digits 1,2,4,6,8 without repetition of digits ?
a. 120 b. 96 c. 56 d. Cannot be determined e. None of these
11. How many 4 digits odd numbers can be formed using the digits 0,1,2,3 if repetition is allowed ?
a. 96 b. 256 c. 192 d. 81 e. None of these
12. Find the total arrangements of the letters of the word APPLE such that A and P does not come together
a. 18 b. 60 c. 45 d. 30 e. None of these
13. A basket contains 6 red, 5 green and 8 blue balls. If four balls are picked at random, what is the probability that all four of them are either red or any two of them are either red or any two out of the four are green ?
a. 5 / 1292 b. 925 / 3876 c. 359 / 1938 d. 11 / 3876
e. none of these
Union bank of India PO 27.11.2005
14. In a container there are 28 eggs out of which 8 eggs are rotten. If two eggs are chosen at random, what will be the probability that at least one egg is rotten ?
a. 94/189 b. 95/187 c. 93/189 d. 97/189 e. None of these LIC Assistant Administrative Officer 12.05.2013
15. A bag contains 2 red, 3 green and 2 blue balls. 2 balls are to be drawn randomly.What is the probability that the balls drawn contain no blue ball ?
a. 5/7 b. 10/21 c. 2/7 d. 11/21 e.None of these
RBI Grade B Officer 17.11.2002
16. If the probability of any event ‘A’ is 0.995, then the probability of Ac ( not having ‘A’ ) is
a. 0.05 b. 0.005 c. 0.105 d. 0.5 e. 0.1
17. From a well shuffled deck of cards, two cards are choosing randomly. Find the probability that both the cards are king or both are queen.
a. 1/121 b. 1/221 c. 2/221 d. 3/221 e. None of these
18. If a dice is thrown thrice, what is the probability that the sum of the number appearing on the dice is greater than 15 ?
a. 5/108 b. 7/216 c. 4/216 d. 5/216 e. None of these
1.A 2.D 3.A 4.D 5.E 6.A 7.B 8.C 9.B 10.B 11.A 12.D 13.B 14.A 15.B 16.B 17.C 18.A