Class Xl ASSIGNMENT

PERMUTATION AND COMBINATION

Q1 How many numbers between 100 & 1000 in which all digits are distinct.

Q2 In how many ways 5 rings of different types can be worn in four fingers.

Q3 How many three digits numbers are there ?

Q4 How many 6 digits number can be formed from the digits 3,1,7,0, 9 & 5 when repetition is not

allowed?

Q5 How many Words with or without meaning can be formed by using the letters of the word TRIANGLE?

Q6 find the different 4 letter word with or without meanings can be formed from the letters of the word

NUMBER ?

Q7 If P(11,r) =P(12,r-1) find r.

Q8 if P(n-1,3):P(n,4)=1:9 find n

Q9 In how many ways can 9 examination papers be arranged so that best and worst paper never

together?

Q10 How many words can be formed from the letters of the word SUNDAY? How many of these begin with

D?

Q11 In how many ways can the letters of the word DELHI be arranged so that vowels occupy even places.

Q12 If all the letters of the Word AGAIN be arranged in a dictionary, What is the 50th word.

Q13 In how many ways can the letters of the word MATHEMATICS be arranged so that vowels are

together.

Q14 In how many ways can the letters of the word ASSASSINATION be arranged so that all s are together.

Q15 Find the no. of words formed by permuting all the letters of following words:

a) PAKISTAN b) RUSSIA c)CONSTANTINOPLE

Q16 How many different signals can be given with 5 different flags by hosting any no. of them at a time.

Q17 There are 6 English 4 Sanskrit and 5 Hindi books. In how many ways can they be arranged so as to

keep all the books of same language together.

Q18 In how many arrangements of the word GOLDEN will the vowels never occur together.

Q19 Out of 5 men and 2 women , a committee of 3 is to be formed. In how many ways can it be formed if

at least one woman is to be included.

Q20 A student has to answer 10questions choosing at least 4 from each part A and B. if there are 6

questions in part A and 7 in B, In how many ways can student choose 10 questions.

Q21 How many different words each containing 2 vowels and 3 consonant can be formed with 5 vowels

and 17 consonants.

Q22 If P(n,r) =720 and C(n,r) = 120. Find r.

Q23 If C(n,r-1):C(n,r):C(n,r+1) =3:4:5 Find n and r.

Q24 In an examination, a Candidate has to pass in each of 5 subjects. In how many ways he can fail.

Q25 Out of 7 Consonants and 4 Vowels, how many words of 3 consonants and 2 vowels can be formed.

Q26 In how many ways can a cricket team be selected from 17 players in which 5 players can bowl? Each

cricket team must include 2 bowlers?

Q27 A man has 6 friends. In how many ways can he invite one or more to a party.

Q28 A bag contains 4 red ,3 white and 2 blue marbles. 3 marbles are drawn at random .find the no. of

ways of selecting at least one white marble in this selection.

Q29 For the post of 5 teachers, there are 23 applicants. 2 post are reserved for SC candidates and there

are 7 SC candidates among the applicants. In how many ways can the selection be made?

Q30 Prove that C(2n,n)=