Question

write all the numbers between 100 and 999 which have same digit at hundreds tens and ones place​

Answer 1

Answer:

Hint: Here we will form all the possible three digit numbers from 100 to 999 such that the number at the unit place of each number so formed is odd.

Hence, we will use the concept of permutation and combination to get the desired answer.

Complete step by step answer:

We know that a number can be formed by using the following digits:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Now we have to form a three digit number between 100 and 999 such that it is odd and has distinct digits i.e. no digits in a number are the same and also the digit at unit’s place of the number is odd.

Let us make three boxes for three digits in the number.

Now we know that one's place can be filled only with odd numbers.

Now we know that the odd numbers from 0 to 9 are 1 , 3, 5, 7, 9

Hence, the one’s place can be filled by 5 ways i.e. the third box can be filled by 5 ways.

Now, the first box i.e. hundreds places can be filled by 8 ways.

Also, since the digits cannot be repeated

Hence, the second box i.e. the tens place can be filled by 8 ways.

Hence, the total number of ways in the three digit odd number can be formed such that it has distinct digits is:-

=8×8×5

=320

ways

Step-by-step explanation:

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