PRESIDIUM GURGAON
ASSIGNMENT-I
SESSION 2024-25
CLASS-XI
SUBJECT- APPLIED MATHEMATICS(241)
CH-6 (PERMUTAIONS AND COMBINATIONS)
CONCEPT BUILDING QUESTIONS - I
1. How many 4-letter words, with or without meaning, can be formed using
all the letters of the word LOGARITHMS, using each letter exactly
once?
2. How many 3 digit even numbers can be formed from the digits, 1, 2, 3, 4,
5, 6 if (a) the digits can be repeated (b) can’t be repeated?
3. How many 5-digit telephone numbers can be constructed using the digits 0
to 9 if each number starts with 67 and no digit appears more than once?
4. Given four flags of different colors, how many different signals can be
generated, if a signal requires the use of two flags one below the other?
5. Find the number of different signals that can be generated by arranging at
least 2 flags in order (one below the other) on a vertical staff, if five different
flags are available.
6. How many five-letter codes can be generated using first 10 letters of the
English alphabet, if no letter can be repeated in the process?
7.An unbiased coin is tossed 4 times in an experiment and the outcomes are
noted. How many possible outcomes are there?
8.How many numbers lying between 100 and 1000 can be formed with the
digits 0, 1, 2, 3, 4, 5 if the repetition of digits is not permitted?
9.How many numbers between 400 and 1000 can be made with the digits 0, 2,
3, 4, 5, 6?
10.Find the number of numbers between 300 and 3000 that can be made with
the digits 0, 1, 2, 3, 4, 5, no digit being repeated in any number.
11.How many numbers greater than 1000 but not greater than 4000 can be
formed with the digits 0, 1, 2, 3, 4, such that repetition of digits is permitted?
1 1 x
12. If find x.
6! 7! 8!
13. If n P4 360 , find n.
14. Find n, if n 1
P4 : n P4 3 : 5, n 4 .
15. Find r, if 5 Pr 2 6 Pr 1 .
16. In how many ways can 4 red, 3 yellow and 2 green discs be arranged in a
row if the discs of the same color are indistinguishable?
17. In how many ways can 8 Indians, 6 Americans and 4 Englishmen be
seated in a row so that all the persons of the same nationality sit together?
18.How many words, with or without meaning, can be formed using all the
letters of the word EQUATION, using each letter exactly once?
19. How many words, with or without meaning, can be made from the letters
of the word ‘SUNDAY’, assuming that no letter is repeated, if
(a) 4 letters are used at a time
(b) all letters are used at a time
(c) all letters are used but first letter is a consonant
(d) 4 letters are used at a time but first letter is a vowel?
20.Find the number of permutations of the letters of the word ALLAHABAD.
21.Find the number of arrangements of the letters of the word
INDEPENDENCE. In how many of these arrangements,
(a) do the words start with P
(b) do all the vowels always occur together
(c) do the vowels never occur together
(d) do the words begin with I and end in P?
22. Find the number of different 8 letter arrangements that can be made from
the letters of the word “DAUGHTER” so that
(a) all vowels occur together
(b) all vowels do not occur together.
23. In how many ways can the letters of the word PERMUTATIONS be
arranged if
(a) the words starts with P and end with S
(b) the vowels are all together
(c) there are always 4 letters between P and S?
24. Find the number of ways of arranging the letters of the word ‘institute’.
25. In how many of the distinct permutations of the letters in the word
“MISSISSIPPI” do the four I’s not come together?
26.In how many ways can the letters of the word “ASSASSINATION” be
arranged so that all the S’s are together?
27.Find the number of rearrangements of the letters of the word
“BENEVOLENT” Also find how many of them end in L?
28.How many different words can be formed with the letters of the word
‘PENCIL’ when vowels occupy even places in the words so formed?
29.In how many ways 7 pictures can be hanged on 9 pegs?
30.Ten buses are plying between two places A and B. In how many ways a
person can travel from A to B and come back?
