Question

17. How many numbers lying between 10 and 1000 can be formed with the digits 2, 3, 4,
O and 7 when no digit is repeated?​

Answer 1

Since the Lower Limit is 10, we don’t have to worry about single digit numbers.

Since the Upper Limit is 1000, we don’t have to worry about any 4 digit numbers.

In short we have to think about 2 digit and 3 digit numbers, greater than 10 and less than 1000.

Since the digits are 2, 3, 4, 0, 8 and 9, any pure 2 digit number (formed out of given digits) would qualify.

For the 2 Digit Numbers:

1st digit could be chosen in 5 ways (excluding 0)

2nd digit could be chosen in 5 ways again (though the digit chosen earlier can’t be repeated, we have zero (0) in lieu of the utilized digit)

Thus we have 5*5 = 25 (Two digit Numbers meeting the criteria)

For 3 digit Numbers:

For 1st digit, we have 5 choices

For 2nd digit, we have 5 choices

For 3rd digit, we have 4 choices

Thus we have 5*5*4 = 100 (Three digit Numbers meeting the criteria)

So, we would have 25+100 = 125 Numbers meeting the required criteria.

125 is the required answer!

Answer 2

If the lcm of two numbers is 216 and there product is 7776, what will be it's hcf