Chapter 7 Permutations and Combinations Ex-7.1 |
Chapter 7 Permutations and Combinations Ex-7.2 |
Chapter 7 Permutations and Combinations Ex-7.4 |

**Answer
1** :

**Answer
2** :

To find four digit number (digits does not repeat)

Now we will have 4 places where 4 digits are to be put.

So, at thousand’s place = There are 9 ways as 0 cannot be at thousand’s place = 9 ways

At hundredth’s place = There are 9 digits to be filled as 1 digit is already taken = 9 ways

At ten’s place = There are now 8 digits to be filled as 2 digits are already taken = 8 ways

At unit’s place = There are 7 digits that can be filled = 7 ways

Total Number of ways to fill the four places = 9 × 9 × 8 × 7 = 4536 ways.

So a total of 4536 four digit numbers can be there with no digits repeated.

**Answer
3** :

Even number means that last digit should be even,

Number of possible digits at one’s place = 3 (2, 4 and 6)

⇒ Number of permutations=

One of digit is taken at one’s place, Number of possible digits available = 5

⇒ Number of permutations=

Therefore, total number of permutations =3 × 20=60.

**Answer
4** :

Total number of digits possible for choosing = 5

Number of places for which a digit has to be taken = 4

As there is no repetition allowed,

⇒ Number of permutations =

The number will be even when 2 and 4 are at one’s place.

The possibility of (2, 4) at one’s place = 2/5 = 0.4

Total number of even number = 120 × 0.4 = 48.

**Answer
5** :

Total number of people in committee = 8

Number of positions to be filled = 2

⇒ Number of permutations =

**Answer
6** :

Find r if

(i)^{5}P_{r} = 2^{6}P_{r-1}

(ii) ^{5}P_{r} = ^{6}P_{r-1}

**Answer
7** :

**Answer
8** :

Total number of different letters in EQUATION = 8

Number of letters to be used to form a word = 8

⇒ Number of permutations =

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,

(ii) All letters are used at a time,

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

**Answer
9** :

(i) Number of letters to be used =4

⇒ Number of permutations =

(ii) Number of letters to be used = 6

⇒ Number of permutations =

(iii) Number of vowels in MONDAY = 2 (O and A)

⇒ Number of permutations in vowel =

Now, remaining places = 5

Remaining letters to be used =5

⇒ Number of permutations =

Therefore, total number of permutations = 2 × 120 =240.

**Answer
10** :

Total number ofletters in MISSISSIPPI =11

Letter Number ofoccurrence

M | 1 |

I | 4 |

S | 4 |

P | 2 |

We take that 4 I’s come together, and they are treated as 1 letter,

∴ Total number of letters=11 – 4 + 1 = 8

⇒ Number of permutations =

Therefore, total number of permutations where four I’s don’t come together = 34650-840=33810

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