Three and four digit numbers are formed from the digits 1 , 3 , 5 , 6 , 8 . If e 1 is number of three digit even numbers with no digit repeated and e 2 is number of four digit even numbers with no digit repeated. Also O 1 represent the number of three digit odd numbers in which no digit is repeated and O 2 represent the number of four digit odd numbers in which no digit is repeated. Then

e 1 + e 2 2 = O 1 + O 2 3 = 6 2

e 1 + e 2 + O 1 + O 2 = 5 P 3 + 5 3

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IMPORTANT

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The total number of positive integral solutions $(x, y, z)$ such that $x y z = 24$ is :

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Important Questions on Permutation and Combination

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 1

If the sum of all numbers greater than

10000

formed by using the digits

0, 1, 2, 4, 5

& no digit being repeated in any number, is

N

, then sum of digits of

N

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Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 2

The number of different seven digit numbers that can be written using only three digits

1, 2

3

under the condition that the digit

2

occurs exactly twice in each number is -

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 3

If there are

N

integers between

100

and

999

, inclusive, have the property that some permutation of its digits is a multiple of

11

between

100

and

999 ?

For example, both

121

and

231

have this property. Then find the value of

\frac{N - 1}{5} .

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 4

Five persons wearing badges with numbers

1, 2, 3, 4, 5

are seated on

5

chairs around a circular table. In how many ways can they be seated so that no two persons whose badges have consecutive numbers are seated next to each other? (Two arrangements obtained by rotation around the table are considered different.)

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 5

The value of

\sum_{r = 0}^{50} {(- 1)}^{r} \frac{{}^{50}C_{r}}{r + 2}

is equal to

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 6

A seven-digit number is in the form of

a b c d e f g

(

g, f, e \dots

etc.,, are digits at the units, tens, hundred place, and so on), where

a < b < c < d > e > f > g

and

a, b, c, e, f, g

are different digits. The number of such numbers is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 7

A guard of

12

men is formed from a group of

n

soldiers. It is found that

2

particular soldiers

A

and

B

are

3

times as often together on guard as

3

particulars soldiers

C, D

and

E

. Then

n

is equal to

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 21 - Permutation and Combination>Level 3>Q 8

The number of permutations of $1, 2, 3, 4, 5, 6, 7, 8$ and $9$ taken all at a time, such that digit $1$ appears some where to the left of digit $2$ and digit $3$ appears to the left of digit $4$ and digit $5$ appears some where to the left of digit $6$ , is (e.g. $815723946$ would be one such permutation)

The total number of positive integral solutions x, y, z such that xyz=24 is :

Important Questions on Permutation and Combination

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The total number of positive integral solutions $(x, y, z)$ such that $x y z = 24$ is :