There are: \(3\times2\times5=30\)combinations

Arrcoding to the context, 4 balls must be put into 4 different tubes that each tube must have a ball. So the free balls are: 7−4=3(balls)

There are: 6.3=18(ways)

 divided by 1 free ball/tube.

There are: 4.3.3=36(ways)

 divided by 2 free ball/tube.

There are: 4.1=4(ways)

divided by 3 free ball/tube.

There are total: 18+36+4=58(ways)

ANSWER: 58 ways

Arrcoding to the context, 4 balls must be put into 4 different tubes that each tube must have a ball. So the free balls are: \(7-4=3\left(balls\right)\)

There are: \(6.3=18\left(ways\right)\) divided by 1 free ball/tube.

There are: \(4.3.3=36\left(ways\right)\) divided by 2 free ball/tube.

There are: \(4.1=4\left(ways\right)\)divided by 3 free ball/tube.

There are total: \(18+36+4=58\left(ways\right)\)

ANSWER: 58 ways

The number of ways to put 4 letters into 5 letter boxes is :

|P45=5!(5−4)!=120

The number of ways to put 4 letters into 5 letter boxes is :

\(|P^4_5=\dfrac{5!}{\left(5-4\right)!}=120\)

There are : (200 - 1) : 1 + 1 = 200 numbers from 1 to 200

We have a sequence of two-digit numbers are as follows :

2 ; 12 ; 22 ; 32 ; ....... ; 192

Apply a formula to count numbers , we have :

(192 - 2) : 10 + 1 = 20 

There are also numbers with 2 digits such as

20 ; 21 ; 23 ; 24 ; .... ; 29 ; 120 ; 121 ; 122 ; 123 ; ...... 129

And there are have 18 also numbers .

So , from these information , we have 38 numbers have digit 2

We have :

200 - 38 = 162 (numbers)

There are 162 numbers from 1 to 200 do not have the digit 2 

There are : (200 - 1) : 1 + 1 = 200 numbers from 1 to 200

We have a sequence of two-digit numbers are as follows :

2 ; 12 ; 22 ; 32 ; ....... ; 192

Apply a formula to count numbers , we have :

(192 - 2) : 10 + 1 = 20 

There are also numbers with 2 digits such as

20 ; 21 ; 23 ; 24 ; .... ; 29 ; 120 ; 121 ; 122 ; 123 ; ...... 129

And there are have 18 also numbers .

So , from these information , we have 38 numbers have digit 2

We have :

200 - 38 = 162 (numbers)

There are 162 numbers from 1 to 200 do not have the digit 2 

There are : (200 - 1) : 1 + 1 = 200 numbers from 1 to 200

We have a sequence of two-digit numbers are as follows :

2 ; 12 ; 22 ; 32 ; ....... ; 192

Apply a formula to count numbers , we have :

(192 - 2) : 10 + 1 = 20 

There are also numbers with 2 digits such as

20 ; 21 ; 23 ; 24 ; .... ; 29 ; 120 ; 121 ; 122 ; 123 ; ...... 129

And there are have 18 also numbers .

So , from these information , we have 38 numbers have digit 2

We have :

200 - 38 = 162 (numbers)

There are 162 numbers from 1 to 200 do not have the digit 2 .

a) There are :7 x 7 x 6 x 5 = 1470 numbers

b) There are :4 x 4 x 3 x 2 = 96 even numbers

a) There are :7 x 7 x 6 x 5 = 1470 numbers

b) There are :4 x 4 x 3 x 2 = 96 even numbers

a) There are :7 x 7 x 6 x 5 = 1470 numbers

b) There are :4 x 4 x 3 x 2 = 96 even numbers

a) There are : 7 x 7 x 6 x 5 = 1470 numbers

b) There are : 4 x 3 x 2 x 1 = 24 old numbers 

ANSWER :

a,There are : 7 x 7 x 6 x 5 = 1470 ( numbers )

b,There are : 4 x 3 x 2 x 1 = 24 ( old numbers )

[hiu]  Easy,right ?

      ANSWER :

a,There are : 7 x 7 x 6 x 5 = 1470 ( numbers )

b,There are : 4 x 3 x 2 x 1 = 24 ( old numbers )

 Easy,right ?