Permutation and Combination HA-12
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Texas A&M University *
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Mathematics
Date
Apr 3, 2024
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Permutation and Combination Home Assignment
Level A
1.
2.
3.
Directions for Questions 4 to 6 : All the letters of the word “RAINBOW” are
arranged in all
possible ways.
4. Find the number of 7-letter words possible, such that each letter is used at most
once.
(A) 1 (B) 24 (C) 120 (D) 7!
5. The number of 7-letter words that begin with R when each letter occurs only once
is
(A) 6 (6!) (B) 7! 2! (C) 6! (D) 2(7!)
6. If each letter is used exactly once, the number of seven letter words which begin
with R and end with W is
(A) 6! (B) 5! (C) 5! 2! (D) 4!
7. Find the number of passwords of length 5 that can be formed using all the vowels
of the alphabet.
8. Using all the letters of the word MOBILE, how many words can be formed, which
begin with M and end with E?
(A) 6 (B) 24 (C) 120 (D) 84
9. How many different words can be formed by using all the letters of the word
INSTITUTE?
10. In how many ways can a cricket team of 11 members be selected from 15
players, so that a particular player is included and another particular player is left
out?
(A) 216 (B) 826 (C) 286 (D) 386
11. A group contains n persons. If the number of ways of selecting 6 persons is
equal to the number of ways of selecting 9 persons, then the number of ways of
selecting four persons from the group is
12. The number of ways of arranging 10 books on a shelf such that two particular
books are always together is
(A) 9! 2! (B) 9! (C) 10! (D) 8
13. The number of 3-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, 6
such that each digit occurs at most once in every number is
14. Find the number of four-digit numbers that can be formed using the digits 1, 2, 3,
4, 5, 6 when each digit can occur any number of times in each number.
15.
16. The number of ways of forming a committee of six members from a group of 4
men and 6 women is
17. The number of distinct lines that can be formed by joining 20 points on a plane,
of which no three points are collinear is
(A) 190 (B) 380 (C) 360 (D) 120
18. Find the number of triangles that can be formed by joining 24 points on a plane,
no three of which are collinear.
(A) 2024 (B) 2026 (C) 2023 (D) 2025
19.
20.
21. In how many ways can seven persons be selected from 6 men, 2 women, 3 boys
and 4 girls?
22. In how many ways can four consonants and three vowels be selected from the letters of the word VALEDICTORY?
(A) 140 (B) 200 (C) 180 (D) 320
23.An eight-letter word is formed by using all the letters of the word “EQUATION”. How many of these words begin with a consonant and end with a vowel?
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24. In how many ways can 6 boys and 5 girls be arranged in a row so that boys and girls sit alternately?
(A) (6!)2 (B) (5!)2 (C) 6! 5!
(D) 2.5! 6!
25. A committee of 5 members is to be formed from a group of 6 men and 4 women. In how many ways can the committee be formed such that it contains more men than
women?
(A) 180 (B) 186 (C) 126 (D) 66
26. How many four-letter words can be formed by using the letters of the word PREVIOUS?
27. In how many ways can ten students be seated around a circular table so that three students always sit together?
(A) 7! (B) 7! 3!
(C) 2.7! (D) 3 (7!)
28. In how many ways can 7 boys and 6 girls be arranged in a row so that no two girls sit together?
(A) 13! (B) 8P6 * 7!
(C) 6! *8P7 (D) 12!
29. In how many ways can 10 boys and 10 girls be arranged in a row so that all the girls sit together?
(A) 10! (B) 11! (C) 20! (D) 10! 11!
Level B 1.
How many words can be formed using all the letters of the word QUESTION
without repetition so that the vowels occupy the even places?
2.
In how many ways can the letters of the word HEPTAGON be permuted so
that the vowels are never separated?
(A) 720 (B) 1440 (C) 5040 (D) 4320
3.
In how many ways can the letters of the word COMBINATION be permuted?
(A) 11! (B) 11! / 2! 2! 2!
(C) 11! / 5! 6!
(D) 11! / 2! 2! 2! 5!
4.
How many four-digit numbers having distinct digits can be formed using the
digits 0 to 9?
(A) 5040 (B) 2526 (C) 3656 (D) 4536
5.
In how many ways can 6 boys and 6 girls sit around a circular table so that no
two boys sit next to each other?
(A) (5!)2 (B) (6!)2 (C) 5! 6! (D) 11!
6.
In how many ways can a panel of 6 doctors be formed from 5 surgeons and 6
physicians if the panel has to include more surgeons than physicians?
(A) 82 (B) 81 (C) 65 (D) 135
7.
A certain group of friends met on a new year eve party and each person
shook hands with everybody else in the group exactly once and the number of
handshakes turned out to be 66. On the occasion of Pongal (harvest festival),
if each person in this group sends a greeting card to every other person in the
group, then how many cards are exchanged?
8.
Find the number of ways of arranging the letters of the word CALENDAR in
such a way that exactly two letters are present in between L and D.
(A) 2640 (B) 3600 (C) 2600 (D) 7200
9.
In how many ways, can the letters of the word EUROPE be arranged so that
no two vowels are together?
(A) 12 (B) 24
(C) 360 (D) Not possible
10.Raju has forgotten his six-digit ID number. He remembers the following: the
first two digits are either 1, 5 or 2, 6, the number is even and 6 appears twice.
If Raju uses a trial and error process to find his ID number at the most, how
many trials does he need to succeed?
(A) 972 (B) 2052 (C) 729 (D) 2051
Answers LEVEL A
Q1 – B , C , D , B , C ,
A
Q9 –D
Q17 – A
Q25 – B
Q2 – 12
Q10 – C
Q18 – A
Q26 – 1680 Q3 – B
Q11 – 1365
Q19 – 1296 , 204
Q27 – B
Q4 – D
Q12- A
Q20 – B , B Q28 – B
Q5 – C
Q13 -120
Q21 – 6435
Q29 – D
Q6 – B
Q14 –D
Q22 – A
Q7 – 3125
Q15 – A , C , Q23 – 10800
Q8 – B
Q16 – 210 Q24 - C
LEVEL B
Q1 – 576
Q6 – B
Q2 – D
Q7 – 132
Q3 – B Q8 – B
Q4 – D
Q9 – D
Q5 - C
Q10 - B
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