Permutation Combination and Probability MCQs with Answers and Solutions for mathematics test and statistics preparation.
Permutation Combination and Probability MCQs
A group consists of 4 men, 6 women and 5 children. In how many ways can 3 men, 2 women and 3 children selected from the given group?
A. 300
B. 450
C. 600
D. 750
A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag?
A. ⁹C₂
B. ³C₂
C. ¹⁶C₂
D. ¹²C₂
In how many ways can three consonants and two vowels be selected from the letters of the word “TRIANGLE”
A. 25
B. 13
C. 40
D. 30
In how many ways can live boys and three girls sit in a row such that all boys sit together?
A. 4800
B. 5760
C. 2880
D. 15000
The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is -.
A. 4000
B. 2160
C. 4320
D. 5300
A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?
A. 20
B. 54
C. 42
D. 60
The number of new words that can be formed by rearranging the letters of the word ‘ALIVE’ is ____?
A. 24
B. 23
C. 119
D. 120
Find the number of ways of arranging the letters of the word “MATERIAL” such that all the vowels in the word are to come together?
A. 720
B. 1440
C. 1860
D. 2160
A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?
A. 300
B. 600
C. 750
D. 900
A group consists of 4 men, 6 women and 5 children. In how many ways can 3 men, 2 women and 3 children selected from the given group?
A. 300
B. 450
C. 600
D. 750
In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
A. 400
B. 500
C. 600
D. 20
A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
A. 63
B. 511
C. 1023
D. 15
A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?
A. ¹²C₅ * 10
B. ¹²C₇ * 10
C. ¹²C₇ * ¹⁰C₅
D. 12 * ¹⁰C₅
A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior?
A. ²²C₁₀
B. ²²C₁₀ + 1
C. ²²C₉ + ¹⁰C₁
D. ²²C₁₀ – 1
Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. How many straight lines, including the first two, can be formed with these points?
A. 29
B. 32
C. 55
D. 30
Groups each containing 3 boys are to be formed out of 5 boys. A, B, C, D and E such that no group can contain both C and D together. What is the maximum number of such different groups?
A. 5
B. 6
C. 7
D. 8
In how many different ways can six players be arranged in a line such that two of them, Asim and Raheem are never together?
A. 120
B. 240
C. 360
D. 480
Three dice (each having six faces with each face having one number from 1 or 6) are ralled. What is the number of possible outcomes such that atleast one dice shows the number 2?
A. 36
B. 81
C. 91
D. 116
Twelve people from a club, by picking lots. One of them will host a dinner for all once in a month. The number of dinners a particular member has to host in one year is________?
A. One
B. Zero
C. Three
D. Cannot be determined
In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position?
A. 9
B. 12
C. 14
D. 18
In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
A. 63
B. 90
C. 126
D. 45
How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed?
A. 40
B. 400
C. 5040
D. 2520
In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?
A. 10080
B. 4989600
C. 120960
D. None of these
In how many different ways can the letters of the word ‘OPTICAL’ be arranged so that the vowels always come together?
A. 120
B. 720
C. 4320
D. 2160
There are 30 people in a group. If all shake hands with one another , how many handshakes are possible?
A. 870
B. 435
C. 30!
D. 29! + 1
A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
A. 21
B. 12
C. 9
D. 108
How many three letter words are formed using the letters of the word TIME?
A. 12
B. 20
C. 16
D. 24
Using all the letters of the word “THURSDAY”, how many different words can be formed?
A. 8
B. 8!
C. 7!
D. 7
Using all the letters of the word “NOKIA”, how many words can be formed, which begin with N and end with A?
A. 3
B. 6
C. 24
D. 120
The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
A. 720
B. 144
C. 120
D. 36
The number of permutations of the letters of the word ‘MESMERISE’ is ___?
A. 9!/(2!)2 3!
B. 9!/(2!)3 3!
C. 9!/(2!)2 (3!)2
D. 5!/(2!)2 3!
A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
A. 150
B. 200
C. 250
D. 300
What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
A. 100
B. 60
C. 30
D. 20
A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?
A. 165
B. 185
C. 205
D. 225
A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most _____?
A. 216
B. 243
C. 215
D. 729
The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is ___?
A. (6!)2
B. 6! * ⁷P₆
C. 2(6!)
D. 6! * 7
How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
A. 360
B. 60
C. 300
D. 180
How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}
A. 60
B. 360
C. 120
D. 240
Also Read: All Important MCQs related to Mathematics