Question

The number of numbers lying between 100 and 1000 can be formed with the digits 1, 2, 3,4, 5, 6, 7 is​

Answer 1

Step-by-step explanation:

here total numbers, 1,2,3,4,5, 6,7. = 7 digits

Between 100 to 1000 contain 3 digit number like101, 124, 588 , 999........

So Total numbers formed

out of 7 digits 3 digits are formed

7×6×5 = 210 ways if digits are not repeating...

and 7×7×7 = 343 ways if numbers are repeating....

Answer 2

Step-by-step explanation:

Since we have to form numbers between 100 and 1000, we need to basically form 3 digit numbers.

_ _ _

So we need to fill these three blanks, by using the numbers available. And since none of them can be repeated, let us fill the first blank. We have 7 choices for the same. For the next blank, since we can't repeat any of the digits, the second blank has 6 choices as one has already been used. And similarly, we have only 5 choices for the third blank.

So the total count of numbers that can be formed are,

= 7 * 6 * 5 = 210.