The number of 4 digit numbers formed using the digits $1, 2, 3, 4, 5, 6, 7$ which are divisible by 4 is

Question

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Answer 1

If number should be divisible by $4$ , last two digits should be divisible
by $4$ .

So the last two digits can be $12, 16, 24, 32, 36, 52, 56, 64, 72, 76 .$

No. of ways $=$ $^{5} P_{2} \times 10 = 200 .$

Answer 2

If number should be divisible by

4

, last two digits should be divisible
by

4

.

So the last two digits can be

12, 16, 24, 32, 36, 52, 56, 64, 72, 76 .

No. of ways

=

^{5} P_{2} \times 10 = 200 .

The number of 4 digit numbers formed using the digits $1, 2, 3, 4, 5, 6, 7$ which are divisible by 4 is

$100$

$150$

$200$

$250$

If number should be divisible by $4$ , last two digits should be divisible
by $4$ .

So the last two digits can be $12, 16, 24, 32, 36, 52, 56, 64, 72, 76 .$

No. of ways $=$ $^{5} P_{2} \times 10 = 200 .$

The number of numbers between $3000$ and $4000$ which are divisible by $5$ , formed by using the digits $3$ , $4$ , $5$ , $6, 7, 8$ is

The number of four digit numbers formed by using the digits $0, 2, 4, 5$ and which are not divisible by $5$ , is

The number of five digit numbers formed using the digits $0, 2, 2, 4, 4, 5$ which are greater than $40, 000$ is

The number of $4$ digit numbers that can be formed with $0, 1, 2, 3, 5$ which are divisible by $2$ or $5$ is

$8$ - digit numbers are formed using the digits $1, 1, 2, 2, 2, 3, 4, 4$ . The number of such numbers in which the odd digits do not occupy odd places, is :

Revise with Concepts

Permutations (n is distinct)

Permutations (n is not distinct)

Types of Permutations

Permutations when Restrictions are given

The number of 4 digit numbers formed using the digits 1,2,3,4,5,6,7 which are divisible by 4 is

100

150

200

250

If number should be divisible by 4, last two digits should be divisible by 4. So the last two digits can be 12,16,24,32,36,52,56,64,72,76. No. of ways = 5P2​×10=200.

The number of numbers between 3000 and 4000 which are divisible by 5, formed by using the digits 3, 4, 5, 6,7,8 is

The number of four digit numbers formed by using the digits 0,2,4,5 and which are not divisible by 5, is

The number of five digit numbers formed using the digits 0,2,2,4,4,5 which are greater than 40,000 is

The number of 4 digit numbers that can be formed with 0,1,2,3,5 which are divisible by 2 or 5 is

8 - digit numbers are formed using the digits 1,1,2,2,2,3,4,4. The number of such numbers in which the odd digits do not occupy odd places, is :

Revise with Concepts

Permutations (n is distinct)

Permutations (n is not distinct)

Types of Permutations

Permutations when Restrictions are given

The number of 4 digit numbers formed using the digits $1, 2, 3, 4, 5, 6, 7$ which are divisible by 4 is

$100$

$150$

$200$

$250$

If number should be divisible by $4$ , last two digits should be divisible
by $4$ .

So the last two digits can be $12, 16, 24, 32, 36, 52, 56, 64, 72, 76 .$

No. of ways $=$ $^{5} P_{2} \times 10 = 200 .$

The number of numbers between $3000$ and $4000$ which are divisible by $5$ , formed by using the digits $3$ , $4$ , $5$ , $6, 7, 8$ is

The number of four digit numbers formed by using the digits $0, 2, 4, 5$ and which are not divisible by $5$ , is

The number of five digit numbers formed using the digits $0, 2, 2, 4, 4, 5$ which are greater than $40, 000$ is

The number of $4$ digit numbers that can be formed with $0, 1, 2, 3, 5$ which are divisible by $2$ or $5$ is

$8$ - digit numbers are formed using the digits $1, 1, 2, 2, 2, 3, 4, 4$ . The number of such numbers in which the odd digits do not occupy odd places, is :