Permutation: n Different Things Taken r at a Time

Q.

How many 3-digit numbers can be formed by using the digits 1 to 9, if no digit is repeated?

Q.

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?

Q.

How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7 if no digit is repeated?

Q. How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that (i) repetition of the digits is allowed? (ii) repetition of the digits is not allowed?

Q. How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?

Q.

In how many of the distinct permutations of the letters in MISSISSIPPI do the four 'I's not come together?

Q. number of permutations of the letters of the word MISSISSIPPI in which four I's do not come together is

1. 840
2. 34310
3. 33810
4. 34560

Q.

If the different permutations of all the letters of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?

Q.

The digit in the unit place of the number

(183!) + $3^{183}$ is

1. 7

2. 3

3. 6

4. 0

Q.

If boys and girls sit alternately then the number of ways in which 3 boys and 3 girls can be seated in a row is

1. 36

2. 72

3. 52

4. 144

Q. 26. the crew of an 8 member boat is to be chosen from 12 men of whom 3 can row on stroke side only.if selected no of ways the crew can be selected is

Q. 17. Number of ways of selecting 3 people from 20 people sitting in a row such that no one of them are consecutive is

Q. The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?

Q. 20. find number of permutation of all the letters of the word MATHEMATICS which start with consonants only

Q.

A $4-$digit number is of the formed by repeating a $2-$digit number such as $2525,3232$ etc. Any number of the form is exactly divisible by :

Q. The number of permutations of the word BIOLOGY is

1. 2520
2. 2000
3. 800
4. 2500

Q.

A dice has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number ‘3’. If dice is rolled once, determine
(i) P(2) (ii) P(1 or 3) (iii) P(not 3)

Q. 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, (ii) there are always 4 letters between P and S?

Q. Which of the following are sets ? Justify your answer.
(i) The collection of all the months of a year beginning with the letter J.
(ii) The collection of ten most talented writers of India.
(iii) A team of eleven best-cricket batsmen of the world.
(iv) The collection of all boys in your class.
(v) The collection of all natural numbers less than $100.$
(vi) A collection of novels written by the writer Munshi Prem Chand.
(vii) The collection of all even integers.
(viii) The collection of questions in this Chapter.
(ix) A collection of most dangerous animals of the world

Q. Find n if

Q.

A five digit number divisible by 3 has to be formed using the numerals 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is

1. 216

2. 240

3. 600

4. 3125

Q. How many words, with or without meaning, can be formed by using all the letters of the word 'DELHI', using each letter exactly once?

Q. How many $3$-digit numbers can be formed from the digits $1,2,3,4$ and $5$ assuming that.

Q. How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

Q. Find the number of $4$-digit even numbers that can be formed using the digits $1,2,3,4,5$ if no digit is repeated. How many of those will be even?

Q. The number of permutations that can be made out of the letters of the word “EQUATION” which start with a consonant and end with a consonant is

1. $2!6!$
2. $3!6!$
3. $3!5!$
4. $2!5!$

Q. 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?

Q. 2. A tea party is arranged for 18 people along two sides of 9 chairs along each side.4 men wish to sit on a particular side & 3 on the other side .in how many ways they can be seated?

Q. In how many ways can be letters of word ASSASSINATION be arranged so that all the S's are together?

Q. 19. If a and b are two distinct real numbers such that ab > 0 , then prove that cosθ ≠ a + b2ab