**Q.7. **Find r if

** (ii) **

**Q.7. **Find r if

** (i)**

** Q.9. **Find n if

**Q.11. **In how many ways can the letters of the word PERMUTATIONS be arranged if the

** (iii)** there are always 4 letters between P and S?

The letters of the word PERMUTATIONS be arranged in such a way that there are always 4 letters between P and S.
Therefore, in a way P and S are fixed. The remaining 10 letters in which 2 T's are present can be arranged in
...

**Q.11. **In how many ways can the letters of the word PERMUTATIONS be arranged if the

** (ii)** vowels are all together?

There are 5 vowels in word PERMUTATIONS and each appears once.
Since all 5 vowels are to occur together so can be treated as 1 object.
The single object with the remaining 7 objects will be 8 objects.
The 8 objects in which 2 T's repeat can be arranged as
ways.
These 5 vowels can also be arranged...

**Q.11. **In how many ways can the letters of the word PERMUTATIONS be arranged if the

**(i) **words start with P and end with S?

There are 2 T's in word PERMUTATIONS, all other letters appear at once only.
If words start with P and ending with S i.e. P and S are fixed, then 10 letters are left.
The required number of arrangements are

**Q.10. **In how many of the distinct permutations of the letters in MISSISSIPPI do the

four I’s not come together?

In the given word MISSISSIPPI, I appears 4 times, S appears 4 times, M appears 1 time and P appear 2 times.
Therefore, the number of distinct permutations of letters of the given word is
...

** Q.9**. How many words, with or without meaning can be made from the letters of the

word MONDAY, assuming that no letter is repeated, if.

** iii**) all letters are used but first letter is a vowel?

There are 6 letters and 2 vowels in word MONDAY.
Therefore, the right most position can be filled by any of these 2 vowels in 2 ways.
Remaining 5 places of the word can be filled using any of rest 5 letters of the word MONDAY.
Hence, the required number of words formed using 5 letters at a time
...

**Q.9. **How many words, with or without meaning can be made from the letters of the

word MONDAY, assuming that no letter is repeated, if.

(ii) all letters are used at a time

There are 6 letters in word MONDAY.
Therefore, words that can be formed using all 6 letters of the word MONDAY.
Hence, the required number of words formed using 6 letters at a time
...

**Q.9. **How many words, with or without meaning can be made from the letters of the

word MONDAY, assuming that no letter is repeated, if.

(i) 4 letters are used at a time

There are 6 letters in word MONDAY.
Therefore, words that can be formed using 4 letters of the word MONDAY.
Hence, the required number of words formed using 4 letters
...

**Q.8. **How many words, with or without meaning, can be formed using all the letters of

** **the word EQUATION, using each letter exactly once?** **

There are 8 different letters in word EQUATION.
Therefore, words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once
is permutations of 8 different letters taken 8 at a time, which is
Hence, the required number of words formed

**Q.5. **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?

From a committee of 8 persons, chairman and a vice chairman are to be chosen assuming one person can not hold more than one position.
Therefore,number of ways of choosing a chairman and a vice chairman is permutations of 8 different objects taken 2 at a time.
Therefore, required number of ways
...

**Q.4. **Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4,5

if no digit is repeated. How many of these will be even?

4-digit numbers that can be formed using the digits 1, 2, 3, 4,5.
Therefore, there will be as many 4-digit numbers as there are permutations of 5 different digits taken 4 at a time.
Therefore, the required number of 4-digit numbers
...

**Q.3. **How many 3-digit even numbers can be made using the digits

1, 2, 3, 4, 6, 7, if no digit is repeated?

3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated.
The unit place can be filled in 3 ways by any digits from 2,4 or 6.
The digit cannot be repeated in 3-digit numbers and the unit place is occupied with a digit(2,4 or 6).
Hundreds, tens place can be filled by remaining any 5 digits.
Therefore, there will be as many 2-digit numbers as there are...

**Q.2. **How many 4-digit numbers are there with no digit repeated?

The thousands place of 4-digit numbers has to be formed by using the digits 1 to 9(0 cannot be included).
Therefore, the number of ways in which thousands place can be filled is 9.
Hundreds,tens, unit place can be filled by any digits from 0 to 9.
The digit cannot be repeated in 4-digit numbers and thousand places is occupied with a digit.
Hundreds, tens, unit place can be filled by remaining...

**Q.1. **How many 3-digit numbers can be formed by using the digits 1 to 9

if no digit is repeated?

3-digit numbers have to be formed by using the digits 1 to 9.
Here, the order of digits matters.
Therefore, there will be as many 3-digit numbers as there are permutations of 9 different digits taken 3 at a time.
Therefore, the required number of 3-digit numbers
...

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