VIBRANT ACADEMY MATHS
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Daily Practice Problems
(India) Private Limited Target IIT JEE-2023
CLASS : XI (MICRO) (Special DPP on Permutation and Combination) DPP. NO.-1
ELEMENTARY PROBLEMS ON PERMUTATION & COMBINATION
NOTE : USE FUNDAMENTAL PRINCIPLE OF COUNTING & ENJOY DOING THE FOLLOWING.
1. In how many ways can clean & clouded (overcast) days occur in a week assuming that an entire
day is either clean or clouded.
2. Four visitors A, B, C & D arrive at a town which has 5 hotels. In how many ways can they disperse
themselves among 5 hotels, if 4 hotels are used to accommodate them.
3. If the letters of the word “VARUN” are written in all possible ways and then are arranged as in a dictionary,
then the rank of the word VARUN is :
(A) 98 (B) 99 (C) 100 (D) 101
4. How many natural numbers are their from 1 to 1000 which have none of their digits repeated.
5. A man has 3 jackets, 10 shirts, and 5 pairs of slacks. If an outfit consists of a jacket, a shirt, and a pair of
slacks, how many different outfits can the man make?
6. There are 6 roads between A & B and 4 roads between B & C.
(i) In how many ways can one drive from A to C by way of B?
(ii) In how many ways can one drive from A to C and back to A, passing through B on both trips ?
(iii) In how many ways can one drive the circular trip described in (ii) without using the same road more than
once.
7. (i) How many car number plates can be made if each plate contains 2 different letters of English
alphabet, followed by 3 different digits.
(ii) Solve the problem, if the first digit cannot be 0. (Do not simplify)
8. (i) Find the number of four letter word that can be formed from the letters of the word HISTORY. (each
letter to be used at most once)
(ii) How many of them contain only consonants?
(iii) How many of them begin & end in a consonant?
(iv) How many of them begin with a vowel?
(v) How many contain the letters Y?
(vi) How many begin with T & end in a vowel?
(vii) How many begin with T & also contain S?
(viii) How many contain both vowels?
9. If repetitions are not permitted
(i) How many 3 digit numbers can be formed from the six digits 2, 3, 5, 6, 7 & 9?
(ii) How many of these are less than 400?
(iii) How many are even?
(iv) How many are odd?
(v) How many are multiples of 5?
10. In how many ways can 5 letters be mailed if there are 3 different mailboxes available if each letter can be
mailed in any mailbox.
sooooooo
Vibrant Academy (I) Pvt. Ltd. "B-41" Road No.2, IPIA, Kota (Raj.) Ph. 06377791915 (www.vibrantacademy.com) [1]
Scotoldmes
Sose
Daily Practice Problems
(India) Private Limited Target IIT JEE-2023
CLASS : XI (MICRO) (Special DPP on Permutation and Combination) DPP. NO.-1
ELEMENTARY PROBLEMS ON PERMUTATION & COMBINATION
NOTE : USE FUNDAMENTAL PRINCIPLE OF COUNTING & ENJOY DOING THE FOLLOWING.
1. In how many ways can clean & clouded (overcast) days occur in a week assuming that an entire
day is either clean or clouded.
2. Four visitors A, B, C & D arrive at a town which has 5 hotels. In how many ways can they disperse
themselves among 5 hotels, if 4 hotels are used to accommodate them.
3. If the letters of the word “VARUN” are written in all possible ways and then are arranged as in a dictionary,
then the rank of the word VARUN is :
(A) 98 (B) 99 (C) 100 (D) 101
4. How many natural numbers are their from 1 to 1000 which have none of their digits repeated.
5. A man has 3 jackets, 10 shirts, and 5 pairs of slacks. If an outfit consists of a jacket, a shirt, and a pair of
slacks, how many different outfits can the man make?
6. There are 6 roads between A & B and 4 roads between B & C.
(i) In how many ways can one drive from A to C by way of B?
(ii) In how many ways can one drive from A to C and back to A, passing through B on both trips ?
(iii) In how many ways can one drive the circular trip described in (ii) without using the same road more than
once.
7. (i) How many car number plates can be made if each plate contains 2 different letters of English
alphabet, followed by 3 different digits.
(ii) Solve the problem, if the first digit cannot be 0. (Do not simplify)
8. (i) Find the number of four letter word that can be formed from the letters of the word HISTORY. (each
letter to be used at most once)
(ii) How many of them contain only consonants?
(iii) How many of them begin & end in a consonant?
(iv) How many of them begin with a vowel?
(v) How many contain the letters Y?
(vi) How many begin with T & end in a vowel?
(vii) How many begin with T & also contain S?
(viii) How many contain both vowels?
9. If repetitions are not permitted
(i) How many 3 digit numbers can be formed from the six digits 2, 3, 5, 6, 7 & 9?
(ii) How many of these are less than 400?
(iii) How many are even?
(iv) How many are odd?
(v) How many are multiples of 5?
10. In how many ways can 5 letters be mailed if there are 3 different mailboxes available if each letter can be
mailed in any mailbox.
sooooooo
Vibrant Academy (I) Pvt. Ltd. "B-41" Road No.2, IPIA, Kota (Raj.) Ph. 06377791915 (www.vibrantacademy.com) [1]
