This document contains multiple permutation and combination problems involving selecting items from groups, arranging letters in words with different constraints, and other counting problems. The problems cover a range of concepts including fundamental counting principles, permutations, combinations, and arrangements.

1. PERMUTATIONS
COMBINATIONS

2. There are 22 boys and 18 girls in a class. The teacher needs to select
one boy and one girl for the post of class monitor. In how many ways
can she do that?
A. 40 B. 4
C. 22 D. 396

3. At a new year party, there were 40 men and 20 ladies. What is the
maximum number of unique dance-pairs that can be formed?
A. 60 B. 800
C. 80 D. 20

4. There are 20 boys in Class X A and 15 boys in Class X B. The head boy of
the school can be chosen from either Section A or Section B. In how
many ways can the head boy be chosen?
A. 30 B. 15
C. 35 D. 300

5. A menu offers 5 starters, 7 main course dishes, and 4 desserts.
a) How many different combinations of dinner can be made, if a dinner
must contain exactly one dish from each course?
b) In the above question, how many combinations are possible, if a
dinner must contain exactly two dishes from each course?

6. A college offers 3 different courses in Physics, 5 different courses in
Mathematics and 4 language courses. A student has to select 2 courses
of Physics, 3 of Mathematics and 1 language course. In how many
different ways can this be done?

7. How many 4-digit numbers are present in the number system?
A. 1000 B. 9000
C. 900 D. 9999

8. Of all the 4-digit numbers, how many numbers have distinct digits?
A. 6561 B. 9000
C. 5040 D. 4536

9. How many 3-digit numbers are possible with the digits – 0, 1, 4, 5, 7
and 9, with and without repetition?

10. How many 4-digit numbers greater than 5000 can be formed using the
digits – 2, 4, 6, 7 and 9, without repetition?

11. How many 4-digits numbers are there which are greater than 2000, but
not greater than 5000?

12. In how many ways can the letters of the following words be arranged?
a) READING b) EDUCATION
c) COMBINE d) STRONG

13. In how many ways can the letters of the following words be arranged,
such that the vowels always come together?
a) TRANSFER
b) ASCENT
c) LEADING
d) ACUMEN
e) WORSHIP

14. In how many ways can the letters of the following
words be arranged?
a) TRANSPORTATION
b) RENAISSANCE
c) CONSTRUCTION
d) COMMUNAL
e) MEDITERRANEAN

15. In how many ways can the letters of the following words be arranged
such that the vowels are always together?
a) MATHEMATICS b) ABACUS
c) SCIENCE d) MANAGEMENT

16. In a certain city, the vehicle numbers are made up of 2 alphabets
followed by 3 numbers. How many such different vehicle numbers are
possible?

17. In how many ways can 3 boys and 5 girls be selected from a group of 7
boys and 9 girls?

18. In how many ways can a committee of 5 people be formed from 4
women and 6 men, such that it contains at least one woman?

19. There are 15 boys and 20 girls in a class.
a) In how many ways can a head boy and a head girl be appointed?
b) In how many ways can a committee of 10 students be formed?
c) In how many ways can a committee of 5 students be formed such
that it has at the most 2 boys?
d) In how many ways can a committee of 7 be formed such that one
particular boy is always selected.

20. In how many ways can 4 boys and 4 girls be seated so that they sit
alternately?
A. 4! B. 8!
C. 4! x 4! D. 4! x 4! x 2!

21. In how many ways can 4 boys and 4 girls be seated such that all the
girls are seated together?
A. 4! x 4! x 2 B. 4! x 5!
C. 5! D. 2 x 5!

22. A box contains 4 white balls, 3 black balls and 3 red balls. In how many
ways can 3 balls be drawn from the box so that at least one black ball is
included in the draw?
A. 75 B. 85
C. 120 D. 63

23. How many different words can be formed using all the letters of the
word “PLETHORA” that begin with P and do not end with R?
A. 5040 B. 40320
C. 4320 D. 720

24. How many diagonals can be formed by joining the vertices of an
octagon?
A. 28 B. 56
C. 64 D. 20

25. There are 20 people who are attending the farewell party. Each of them
shakes hands with all the others. How many hand-shakes take place in
the party?
A. 200 B. 40
C. 190 D. 100

26. In a certain area, all telephone numbers have eight digits. The first
three digits are always 278 or 279 or 275. The maximum number of
telephone numbers having all the eight digits distinct and with the
above conditions is :
A. 3125 B. 2520
C. 7560 D. 7776