Question

How many numbers can be made which lie between 400 and 900 by using digits 1,2,3,5,6,8 and 0 without repetition?

Answer 1

Answer:

90

Step-by-step explanation:

First place by 5,6,8 means 3 ways

Second place by 6 ways

Third place by 5 ways

Therefore,3×6×5=90

Answer 2

Answer:

The total number which lies between 400 and 900 by using the digits 1,2,3,5,6,8, and 0 without repetition is 90

Explanation:

Given:

The digits to be used i.e. 1,2,3,5,6,8 and 0 to be used without repetition

To Find:
How many numbers can be made that lie between 400 and 900 by using the given digits

Chapter:

Permutation And Combination

Solution:

A number between 400 and 900 is three-digit i.e. _ _ _

First place, can be filled with 5,6, and 8 only.

As the number must be greater than 400 and cannot begin with 0 causing the numbers 0,1,2, and 3 to not be used.

Thus, there are 3 ways.

The second place,

Can be filled in only 6 ways i.e. 1,2,3,0 and two from 5,6,8

The third place,

Can be filled in 5 ways i.e. 4 from 1,2,3,0 and one from 5,6,8

Thus, there are 5 ways.

Now, the permutations or all the possible combinations are,

$5*6*3=90$

Conclusion:

Thus, the total number which lies between 400 and 900 by using the digits 1,2,3,5,6,8, and 0 without repetition is 90

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