Questions for practice:
(Choose correct one)
1. Out of 7 consonants and 4 vowels, how many words
of 3 consonants and 2 vowels can be formed?
A. 24400. B. 21300
C. 210 D. 25200
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2. In a group of 6 boys and 4 girls, four children are to
be selected. In how many different ways can they be
selected such that at least one boy should be there?
A. 159. B. 209
C. 201. D. 212
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3. From a group of 7 men and 6 women, five persons
are to be selected to form a committee so that at least 3
men are there in the committee. In how many ways can
it be done?
A. 624 B. 702
C. 756. D. 812
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4. In how many different ways can the letters of the
word 'OPTICAL' be arranged so that the vowels always
come together?
A. 610 B. 720
C. 825 D. 920
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5. In how many different ways can the letters of the
word 'CORPORATION' be arranged so that the vowels
always come together?
A. 47200 B. 48000
C. 42000 D. 50400
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6. 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. 1 B. 126
C. 63 D. 64
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7. In how many different ways can the letters of the
word 'MATHEMATICS' be arranged such that the
vowels must always come together?
A. 9800 B. 100020
C. 120960 D. 140020
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8. There are 8 men and 10 women and you need to
form a committee of 5 men and 6 women. In how many
ways can the committee be formed?
A. 10420 B. 11
C. 11760 D. None of these
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9. How many 3-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. 720 B. 420
C. None of these D. 5040
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10. In how many different ways can the letters of the
word 'LEADING' be arranged such that the vowels
should always come together?
A. None of these. B. 720
C. 420 D. 122
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11. A coin is tossed 3 times. Find out the number of
possible outcomes.
A. None of these B. 8
C. 2 D. 1
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12. In how many different ways can the letters of the
word 'DETAIL' be arranged such that the vowels must
occupy only the odd positions?
A. None of these B. 64
C. 120 D. 36
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13. A bag contains 2 white balls, 3 black balls and 4 red
balls. In how many ways can 3 balls be drawn from the
bag, if at least one black ball is to be included in the
draw?
A. 64 B. 128
C. 32 D. None of these
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14. In how many different ways can the letters of the
word 'JUDGE' be arranged such that the vowels always
come together?
A. None of these B. 48
C. 32 D. 64
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15. In how many ways can the letters of the word
'LEADER' be arranged?
A. None of these B. 120
C. 360 D. 720
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16. How many words can be formed by using all letters
of the word 'BIHAR'?
A. 720 B. 24
C. 120 D. 60
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17. How many arrangements can be made out of the
letters of the word 'ENGINEERING' ?
A. 924000 B. 277200
C. None of these D. 182000
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18. How many 3 digit numbers can be formed from the
digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and
none of the digits is repeated?
A. 20 B. 16
C. 8 D. 24
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19. How many words with or without meaning, can be
formed by using all the letters of the word, 'DELHI'
using each letter exactly once?
A. 720 B. 24
C. None of these D. 120
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20. What is the value of P(100,2) ?
A. 9801 B. 12000
C. 5600 D. 9900
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21. In how many different ways can the letters of the
word 'RUMOUR' be arranged?
A. None of these B. 128
C. 360 D. 180
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22. There are 6 periods in each working day of a school.
In how many ways can one organize 5 subjects such
that each subject is allowed at least one period?
A. 3200 B. None of these
C. 1800 D. 3600
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23. How many 6 digit telephone numbers can be
formed if each number starts with 35 and no digit
appears more than once?
A. 720 B. 360
C. 1420 D. 1680
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24. An event manager has ten patterns of chairs and
eight patterns of tables. In how many ways can he
make a pair of table and chair?
A. 100 B. 80
C. 110 D. 64
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25. 25 buses are running between two places P and Q. In
how many ways can a person go from P to Q and return
by a different bus?
A. None of these B. 600
C. 576 D. 625
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26. A box contains 4 red, 3 white and 2 blue balls. Three
balls are drawn at random. Find out the number of
ways of selecting the balls of different colours?
A. 62 B. 48
C. 12 D. 24
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27. A question paper has two parts P and Q, each
containing 10 questions. If a student needs to choose 8
from part P and 4 from part Q, in how many ways can
he do that?
A. None of these B. 6020
C. 1200 D. 9450
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28. In how many different ways can 5 girls and 5 boys
form a circle such that the boys and the girls alternate?
A. 2880 B. 1400
C. 1200 D. 3212
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29. Find out the number of ways in which 6 rings of
different types can be worn in 3 fingers?
A. 120 B. 720
C. 125 D. 729
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30. In how many ways can 5 man draw water from 5
taps if no tap can be used more than once?
A. None of these B. 720
C. 60 D. 120
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