Exercise 14.5
Page no 14.54
Question 1
Four books, one each in chemistry, physics, biology and mathematics, are to be arranged in a shelf. In how many ways can this be done?
Question 2
There are 6 candidates contesting for a certain office in a municipal election. In how many ways can their names be listed on a ballot paper ?
Question 3
How many different signals can be generated from 6 flags of different colours if each signal makes use of all the flags at a time, placed one below the other?
Question 4
Seven songs are to be rendered in a Programme . In how many different orders could they be rendered ?
Question 5
Ten horses are running a race. In how many ways can these horses come in the first, second and third place, assuming no tics ?
Question 6
Six candidates are called for interview to fill four posts in an office. Assuming that each candidate is fit for each post, determine the number of ways in which
(i) first and second posts can be filled.
(ii) first three posts can be filled.
(iii) all the four posts can be filled.
Question 7
From a pool of 12 candidates, in how many ways can we select president, vice president, secretary and a treasurer if each of the 12 candidates can hold any office?
Question 8
From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?
Question 9
In how many ways can 4 red , 3 yellow and 2 green discs e arranged in a row if the disc of the same colour are indistinguishable ?
Page no 14.55
Question 10
Find the sum of all the 4 digit numbers that can be formed with the digits $3,2.3,4$
Question 11
In the given figure we see that it has 4 horizontal blocks (or paths) and 3 vertical blocks (or paths). This is known as $4 \times 3$ grid. Seema wishes to go from $A$ to $B$, but the instruction is that she must go only on the right and only up, but not necessarily in that order. How many possible paths does she have at her disposal ?
.(Diagram to be added)
Question 12
How many signals can be made by hoisting 2 blue, 2 red and 5 yellow flags on a pole at the same time.
Question 13
How many different signals can be made by hoisting 6 differently coloured flags one above the other when any number of them may be hoisted at once?
Question 14
Find the number of arrangements of the letters of the word 'Delhi' if $e$ ' always comes before $i$.
Question 15
(i) Find the number of different arrangements (permutations) of the letters of the word "BANNANA."
(ii) Find the number of permutations of the letters of the word ALLAHABAD.
Question 16
How many words can be formed from the letters of the word 'CIRCUMFERENCE' taken all together?
Question 17
Find the number of permutations of the letters of the word " I N D E P E N D E N C
In how many of these arrangements ?
(i) do the words start with $P$ ?
(ii) do all the vowels always occur together?
(iii) do the vowels never occur together?
(iv) do the words begin with $I$ and end in $P$.
Question 18
How many different words can be formed with the letters of the word 'VICE-CHANCELLOR' so that the vowels are together?
Question 19
How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if
(i) 4 letters are used at a time ?
(ii) all letters are used at a time ?
(iii) all letters are used but the first letter is a vowel?
Question 20
How many words can be formed using all letters of the word, EQUATION, so that
(i) each letter occurs exactly once?
[HOTS]
(ii) vowels and consonants occur together?
Question 21
The letters of the word TUESDAY are arranged in a line. each arrangement ending with letter $S$. How many different arrangements are possible ? How many of them stant with letier $D$ ?
Page no 14.56
Question 22
Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so that
(i) all vowels occur together,
(ii) all vowels do not occur together.
Question 23
How many different words can be formed with the letters of the wond "MATHEMATICS'"? In how many of them the vowels are together and consonants are together ?
Question 24
In how many ways can the letters of the word 'MUZAFFARPUR' be rearranged? How many such words will begin with $M$ ?
Question 25
In how many ways can the letters of the word ASSASSINATION be arranged so that all the $S$ 's are together ?
Question 26
In how many ways can the letters of the word 'BANARAS' be arranged so that the letters $N$ and $S$ are never together ?
Question 27
In how many ways can the letters of the word 'PLANTAIN' be arranged so that the two ' $A$ ' do not come together?
Question 28
Find the number of words that can be made by arranging the letters of the word "INTERMEDIATE' so that
(i) The relative order of vowels and consonants do not change.
[HOTS
(ii) The order of vowels do not change.
Question 29
In how many permutations of the letters of the word 'PARALLEL' all the $L$ do not come together?
Question 30
Find the number of words formed by the letters of the word ' $D E L H I$ which
(i) begin with $D$
(ii) end with $I$
(iii) the letter $L$ being always in the middle
(iv) begin with $D$ and end with $I$.
Question 31
In how many ways can the letters of the word "VIOLENT' be arranged so that vowels occupy only the odd places ?
Question 32
In how many different ways can the letters of the word 'SALOON' be arranged if the consonants and vowels must occupy alternate places ?
Question 33
How many words can be formed out of the letters of the word ' $A R T I C L E^{\prime}$ so that the vowels occupy the even places.
Question 34
(i) Find the number of words formed, with the letters of the word 'DELHI' when any letter may be repeated any number of times.
(ii) Find the number of 4 letter words, with or without meaning, which can be formed out of the letters of the word 'ROSE' where
(a) the repetition of the letters is not allowed.
(b) repetition of the letters is allowed.
Question 35
How many words can be formed by using the letters of the word 'BHARAT'' How many of these words will not contain $B$ and $H$ together. How many of these start with $B$ and end with $T$ ?
Question 36
In how many ways can the letters of the word 'IVTERMEDIATE be arranged among themselves so that no two vowels may occupy consecutive places ?
Question 37
In how many ways can the letters of the word 'PERMUTATIONS' be arranged if the (i) words start with $P$ and end with $S$ ?
(ii) vowels are all together, (iii) there are always 4 letters between $P$ and $S$.
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